In a large mixing bowl, combine the all-purpose flour, granulated sugar, and salt. Cut in the cold, cubed unsalted butter until the mixture resembles coarse crumbs. Stir in the egg yolk and cold water until a dough forms. Press the dough into a tart or cake pan and chill for 20-30 minutes.

Preheat your oven to 350°F (175°C). Prick the bottom of the chilled crust with a fork and bake for 12-15 minutes until lightly golden. Allow to cool slightly on a wire rack.

In a medium saucepan, whisk together the granulated sugar, cornstarch, egg yolks, and lemon zest until smooth. Gradually pour in the milk while whisking continuously. Cook over medium heat, stirring frequently until thickened, about 5-7 minutes. Remove from heat and stir in lemon juice, unsalted butter, and vanilla until combined.

Pour the custard into the pre-baked crust. Bake for 25-30 minutes until the edges are set but the center remains jiggly. Allow to cool completely.

Refrigerate the cake for at least 4 hours to set. Dust with powdered sugar before serving. Slice and enjoy with fresh berries or whipped cream.