Cube 1 stick unsalted butter and place in a small bowl. Freeze for 5 minutes while you prepare the wet and dry ingredients.

Place 1 large egg yolk, 1 tablespoon heavy cream, and 1 teaspoon vanilla extract in a small bowl and whisk with a fork to combine. Place 1 ¼ cups all-purpose flour, ⅔ cup powdered sugar, and ½ teaspoon kosher salt in a food processor fitted with the blade attachment. Pulse a few times to combine.

Scatter the cold pieces of butter over the flour mixture. Pulse until the mixture is like coarse sand, about 15 (1-second) pulses.

With the motor running, pour the egg mixture through the tube and process until big clumps of dough form, 20 to 30 seconds.

Transfer the dough to a sheet of parchment paper and gather into a smooth disc. Top with a second sheet of parchment paper and roll the dough into an 11-inch round that’s a little thicker than ⅛-inch. Slide the dough (still in the parchment) onto a baking sheet and freeze for 5 minutes.

Uncover the dough (reserve one of the parchment sheets) and transfer the dough into a 9-inch round tart pan with removable bottom. Gently ease and then press it into the sides and onto the bottom of the pan, making sure it fits snugly into the corners. Trim off any excess dough by running the rolling pin over the top of the pan. Freeze the tart shell 30 minutes.

Finely grate the zest of 4 to 5 medium lemons until you have ¼ cup loosely packed. Halve and juice the lemons until you have ⅔ cup. Place the zest and juice in a large heatproof bowl. Heat the oven to 375ºF.

When the crust is ready, press the reserved sheet of parchment paper onto the crust and fill with pie weights. Bake until set, about 30 minutes.

Remove the weights and parchment. Bake until just starting to turn light golden brown at the edges, about 5 minutes. Place the baking sheet on a wire rack while making the filling.

Fill a large saucepan with about 1 ½ inches water and bring to a simmer over medium heat. Fit a fine-mesh strainer over a medium bowl.

Add 7 large egg yolks, 2 large eggs, 1 cup granulated sugar, ¼ teaspoon kosher salt to the lemon zest and juice and whisk to combine. Cut 4 tablespoons unsalted butter into 4 pieces and add to the lemon mixture.

Place the bowl onto the saucepan of simmering water and cook, stirring constantly until it thickens slightly to the consistency of cold heavy cream and registers 170ºF, 7 to 8 minutes. Remove from heat.

Stir in 3 tablespoons cold heavy cream. Pour the mixture through the fine-mesh strainer and discard the contents of the strainer.

Pour the filling into the warm crust. If there are any bubbles in the filling, gently pick up the pan and tap it against the counter. Bake until the center jiggles slightly but the rest of the filling is set, 10 to 15 minutes.

Place the baking sheet on a wire rack and let the tart cool completely, about 1 hour. Remove the outer ring and garnish with powdered sugar or whipped cream and candied lemon peel. Cut into slices and serve.