In a large mixing bowl, whisk the flour, sugar and salt until well combined. Add the cold, cubed butter.
Using your fingers or a pastry cutter, work the butter into the flour until the mixture resembles coarse crumbs.
Gradually add cold water, one tablespoon at a time, until the dough comes together. Be careful not to over-mix. Form the dough into a ball, wrap it in plastic wrap, and refrigerate for at least 30 minutes to 1 hour.
Preheat oven to 350 F.
Meanwhile, In a bowl, whisk together the egg yolks, evaporated milk, condensed milk, and vanilla extract until well combined.
On a floured surface, roll out the chilled dough to about ⅛-inch thickness. Using a round cookie cutter or a glass, cut circles from the rolled-out dough. Press each circle into the wells of a mini muffin tin to form the crusts.
Prick the bottom of the crust with fork before adding the filling to prevent crust puffing up.
Pour the egg mixture into each crust, filling them almost to the top.
Bake the mini egg pies in the oven for about 15-20 minutes or until the filling is set and the tops are lightly browned.
Allow the mini egg pies to cool in the muffin tin for a few minutes before transferring them to a wire rack to cool completely.