Paris-Brest

Praline: Line rimmed baking sheet with parchment paper; spray parchment with vegetable oil spray and set aside. Bring sugar, water, and lemon juice to boil in medium saucepan over medium heat, stirring once or twice to dissolve sugar. Cook, without stirring, until syrup is golden brown, 10 to 15 minutes. Remove saucepan from heat, stir in hazelnuts, and immediately pour mixture onto prepared sheet. Place sheet on wire rack and allow caramel to harden, about 30 minutes.

Break hardened caramel into 1- to 2-inch pieces; process pieces in food processor until finely ground, about 30 seconds. Add oil and salt and process until uniform paste forms, 1 to 2 minutes. Transfer mixture to bowl, cover with plastic wrap, and set aside.

Pastry Dough: Adjust oven racks to upper-middle and lower-middle positions and heat oven to 400 degrees. Draw or trace 8-inch circle in center of two 12 by 18-inch sheets of parchment paper; flip parchment over. Spray 2 baking sheets with vegetable oil spray and line with parchment (keeping guide rings on underside).

Beat eggs in measuring cup or small bowl; you should have about 1 cup (discard any excess over 1 cup). Heat butter, milk, water, sugar, and salt in medium saucepan over medium heat, stirring occasionally. When butter mixture reaches full boil (butter should be fully melted), immediately remove saucepan from heat and stir in flour with heat-resistant spatula or wooden spoon until combined and no mixture remains on sides of pan. Return saucepan to low heat and cook, stirring constantly, using smearing motion, until mixture is slightly shiny and tiny beads of fat appear on bottom of saucepan, about 3 minutes.

Immediately transfer butter mixture to food processor and process with feed tube open for 30 seconds to cool slightly. With processor running, gradually add eggs in steady stream. When all eggs have been added, scrape down sides of bowl, then process for 30 seconds until smooth, thick, sticky paste forms.

Transfer ¾ cup dough to pastry bag fitted with ⅜-inch round tip. To make narrow inner ring, pipe single ½-inch-wide circle of dough directly on traced guide ring on 1 baking sheet. For large outer ring, squeeze out any excess dough in pastry bag and change pastry bag tip to ½-inch star tip. Put all remaining dough into pastry bag. Pipe ½-inch-wide circle of dough around inside of traced guide ring on remaining baking sheet. Pipe second ½-inch circle of dough around first so they overlap slightly. Pipe third ½-inch circle on top of other 2 circles directly over seam. Discard any excess dough. Sprinkle hazelnuts evenly over surface of ring.

Place sheet with larger outer ring on upper rack and sheet with narrow inner ring on lower rack and bake until narrow ring is golden brown and firm, 22 to 26 minutes. Remove narrow ring and transfer to wire rack. Reduce oven temperature to 350 degrees and continue to bake larger ring for 10 minutes. Remove sheet from oven and turn off oven. Using paring knife, cut 4 equally spaced ¾-inch-wide slits around edges of larger ring to release steam. Return larger ring to oven and prop oven door open with handle of wooden spoon. Let ring stand in oven until exterior is crisp, about 45 minutes. Transfer ring to wire rack to cool, about 15 minutes.

Cream Filling: Sprinkle gelatin over water in small bowl and let sit until gelatin softens, about 5 minutes. Heat half-and-half in medium saucepan over medium heat until just simmering. Meanwhile, whisk egg yolks and sugar in medium bowl until smooth. Add flour to yolk-sugar mixture and whisk until incorporated. Remove half-and-half from heat and, whisking constantly, slowly add ½ cup to yolk-sugar mixture to temper. Whisking constantly, add tempered yolk-sugar mixture back to half-and-half in saucepan.

Return saucepan to medium heat and cook, whisking constantly, until yolk-sugar mixture thickens slightly, 1 to 2 minutes. Reduce heat to medium-low and continue to cook, whisking constantly, for 8 minutes.

Increase heat to medium and cook, whisking vigorously, until bubbles burst on surface, 1 to 2 minutes. Remove saucepan from heat; whisk in butter, vanilla, and softened gelatin until butter is melted and incorporated. Strain pastry cream through fine-mesh strainer set over large bowl. Press lightly greased parchment paper directly on surface and refrigerate until chilled but not set, about 45 minutes.

Using stand mixer fitted with whisk, whip cream on medium-low speed until foamy, about 1 minute. Increase speed to high and whip until soft peaks form, 1 to 3 minutes. Whisk praline paste and half of whipped cream into pastry cream until combined. Gently fold in remaining whipped cream until incorporated. Cover and refrigerate until set, at least 3 hours or up to 24 hours.

Using serrated knife, slice larger outer ring in half horizontally; place bottom on large serving plate. Fill pastry bag fitted with ½-inch star tip with cream filling. Pipe ½-inch-wide strip of cream filling in narrow zigzag pattern around center of bottom half of ring. Press narrow inner ring gently into cream filling. Pipe cream filling over narrow ring in zigzag pattern to cover. Place top half of larger ring over cream filling, dust with confectioners' sugar, and serve. (Cooled pastry rings can be wrapped tightly in plastic wrap and stored at room temperature for up to 24 hours or frozen for up to 1 month. Before using, recrisp rings in 300-degree oven for 5 to 10 minutes. Praline can be made up to 1 week in advance and refrigerated. Let praline come to room temperature before using. Pastry dough can be transferred to bowl, with surface covered with sheet of lightly greased parchment paper, and stored at room temperature for up to 2 hours. Dessert can be assembled and kept in refrigerator up to 3 hours in advance.)