In a mixing bowl, combine all-purpose flour, granulated sugar, and a pinch of salt. Cut in the chilled, cubed unsalted butter using a pastry cutter until the mixture resembles coarse crumbs. Mix in the egg yolk and just enough cold water to form a dough. Press this dough into a tart or cake pan, smoothing it evenly, and chill for 20-30 minutes.

Preheat your oven to 350°F (175°C). Take the chilled crust from the refrigerator and prick the bottom with a fork to prevent bubbling. Bake for 12-15 minutes until the edges are lightly golden. Once baked, remove from the oven and let it cool completely in the pan while you prepare the filling.

In a medium saucepan over medium heat, whisk together granulated sugar, cornstarch, lemon zest, and egg yolks until well combined. Gradually stir in whole milk, continuing to whisk vigorously as you cook. Keep stirring until the mixture thickens and becomes glossy, about 5-7 minutes. Remove from heat and stir in fresh lemon juice, unsalted butter, and vanilla extract until smooth.

Pour the lemon custard filling into the cooled crust, spreading it evenly. Bake for 25-30 minutes until the custard is set but still jiggly in the center.

Allow the cake to cool at room temperature for about 30 minutes. Transfer the cake to the refrigerator and chill for at least 2-4 hours, or overnight for best flavor.