Instructions

For the Tart Dough: Whisk egg yolk and cream together in small bowl and set aside. Process sugar, hazelnuts, and salt in food processor until fine and powdery, about 1 minute. Add butter and process until smooth and creamy, scraping down sides of bowl as needed, about 1 minute. Gradually add egg mixture and process until smooth and combined, scraping down sides of bowl as needed, about 1 minute. Add flour and process until mixture forms cohesive dough, about 30 seconds. Transfer dough to counter and briefly knead until smooth. Roll dough between 2 large sheets of parchment paper into 12-inch round. Transfer dough, still between parchment, to baking sheet and freeze until cold and stiff, about 15 minutes. (Alternatively, you can pop it into the fridge for 30 minutes.)
Transfer dough to counter, discard top sheet of parchment, and lightly dust dough with flour. When dough is slightly pliable, 1 to 3 minutes, ease dough over rolling pin and roll it up loosely, peeling away bottom sheet of parchment. Unroll dough on top of tart pan and ease dough into pan by gently lifting edge of dough with your hand while pressing into corners with your other hand. Gently press dough into fluted sides of pan, forming distinct seam along pan circumference. Run rolling pin over top of pan to remove excess dough. (See photos below for details.) Place dough-lined pan on baking sheet, cover with plastic wrap, and refrigerate for at least 30 minutes or up to 3 days. (Dough-lined pan can be wrapped tightly with plastic wrap and frozen for up to 1 month.)
Adjust oven rack to middle position and heat oven to 325 degrees F/160 degrees C. Remove dough-lined pan from refrigerator and, using skewer, poke 30 small holes, evenly spaced, in dough on bottom. Bake tart shell on baking sheet until edges just begin to brown, 20 to 25 minutes, rotating pan halfway through baking. Remove tart shell from oven and let cool while preparing filling.
For the Chocolate Filling: Combine 2 cups water and ice cubes in large bowl to make ice bath. Place chocolate, ½ cup plus 1 tablespoon water, sugar, and salt in metal or glass bowl over saucepan of simmering water. Cook, stirring frequently with rubber spatula, until chocolate is fully melted and smooth, about 5 minutes. Transfer bowl to ice bath and chill, stirring constantly, until mixture is slightly thickened and registers between 75 and 80 degrees F/24 and 27 degrees C, 30 to 60 seconds. Remove bowl from ice bath and continue to stir 30 seconds longer. Transfer filling to cooled tart shell and tap baking sheet lightly on counter to release air bubbles; refrigerate tart until set, about 1 hour. (Tart can be wrapped in plastic wrap and refrigerated for up to 24 hours.)
For Matcha Whipped Cream: In bowl of stand mixer fitted with whisk attachment, whip cream, sugar, and salt on high speed until soft peaks form. Add 3 teaspoons matcha, reduce speed to medium, and whip until stiff peaks form. Remove tart from refrigerator. Remove outer metal ring of tart pan, slide thin metal spatula between tart and pan bottom, and carefully slide tart onto serving platter. Spread whipped cream evenly over chocolate layer. Using fine-mesh strainer, dust tart with 1 teaspoon matcha. Sprinkle with pomegranate seeds, cut into wedges, and serve.