Step 1

For the butter dough: Put the flour and butter in a food processor and process to a thick, smooth paste, about 2 minutes. Transfer the dough to plastic wrap using a metal spoon and shape into a 5-inch square. Chill in the refrigerator until needed.

Step 2

For the water dough: Put the flour, sugar, salt and 3 tablespoons of the beaten egg in the same food processor (reserve the remaining beaten egg for the egg filling). Pulse a few times to combine. Stream in the cold water while pulsing until a ball forms that is shaggy and not sticky, about 2 minutes. Wrap the dough into a rough square with plastic wrap and chill in the freezer for 20 minutes.

Step 3

For the egg filling: While the doughs are resting, put the milk and sugar in a small pot and heat over high heat until the sugar is dissolved, about 1 minute. Let cool completely, about 5 minutes.

Step 4

Whisk together the eggs and reserved beaten egg in a large bowl until no visible egg whites remain, about 1 minute. Whisk in the evaporated milk, vanilla extract and cooled milk mixture. Strain the filling through a fine-mesh sieve twice into a 2-cup liquid measuring cup with a spout. Skim off any foam on the surface of the egg filling. Wrap the measuring cup with plastic wrap and chill in the refrigerator until needed.

Step 5

Prepare the pastry: Roll the water dough on a lightly floured surface using a rolling pin to a 10-inch square. Position the butter dough in the center of the water dough in the shape of a diamond. Wrap the outer dough around the butter layer and seal in the edges; make sure to brush away excess flour with a pastry brush. Roll the dough out to a 6-by-12-inch rectangle. Fold both short sides toward the center and then fold in half like closing a book. Wrap in plastic and chill in the freezer for 20 minutes.

Step 6

Roll out the dough to a 6-by-12-inch rectangle with the smooth side of the dough to the left side. Fold both short sides toward the center and then fold in half like closing a book. Wrap in plastic wrap and chill in the freezer for 20 minutes. Repeat this process of folding and resting one more time.

Step 7

After the final 20-minute rest, roll out the dough on a lightly floured surface to an 11-by-14-inch rectangle, slightly thinner than 1/4-inch thickness. Cut out 12 rounds of dough using a 3 1/4-inch round cutter. Stack the rounds with plastic wrap between each layer and chill in the freezer until firm, about 10 minutes.

Step 8

Center one dough round onto each of twelve 3-inch egg tart molds and press the dough up the edges of each mold from the bottom to the top, thinning out the bottom. Put the egg tart molds on the prepared baking sheet. Dock the bottom of each dough round 3 times using the tines of a fork. Chill in the refrigerator until firm, about 30 minutes.

Step 9

Adjust an oven rack to the lowest position and preheat the oven to 375 degrees F.

Step 10

Carefully pour the egg filling into the 12 tart shells (about 1 1/2 tablespoons in each; there should be about 1/4 inch of space between the egg filling and top edges of the crust). Bake the egg tarts until the crusts are starting to brown around the edges, 20 to 22 minutes. Reduce the oven temperature to 350 degrees F and continue to bake until the crusts are light golden brown and the fillings have puffed slightly, 13 to 15 minutes. Let cool in the oven with the door ajar until the egg filling gently settles back down, about 5 minutes. Transfer the baking sheet to a wire rack until cool enough to handle, about 15 minutes. Remove the egg tarts from the molds and enjoy slightly warm or completely cooled.