In a food processor, pulse the flour, sugar, and butter until the mixture resembles coarse crumbs. Add the egg yolk and 1 tablespoon of cold water, pulsing until the dough comes together. Add an additional tablespoon of water if needed. Press the dough into mini tart pans and refrigerate for 30 minutes.
Whisk together eggs, egg yolks, sugar, lemon juice, and lemon zest in a saucepan over medium heat. Stir in the melted butter. Cook, stirring constantly, until the mixture thickens, about 5-7 minutes. Strain through a fine sieve.