Place the flour, sugar, butter, and salt in a food processor equipped with the blade attachment and work it to get a crumbly mixture.
Add the egg yolks, milk, and the lemon zest, or the vanilla, and keep mixing by pulsing the mixture only to the point where the dough becomes cohesive.
If the dough is too sticky, add one tablespoon of flour. If too dry and crumbly, add 1 tbsp milk. Do not overwork the dough, as you want it to be flaky.
Flatten the dough into a 2-inch-thick disk, to make it easier to open it later on. Wrap the disk in plastic wrap and keep in the fridge for a couple of hours.
In the meantime, prepare the filling of your choice. Some suggestions are given on the bottom.
Preheat the oven to 350F. Remove the dough from the fridge and bring to room temperature so you can easily roll it out, without cracking the dough. Roll out the dough to 1/8 inch in thickness. Use a 3 ½ inch wide drinking glass or a round cookie cutter to cut round disks. Try to leave as little room as possible between disks, to avoid reusing much of the dough. The less you work the dough, the flakier the cookies will be.
Spoon 1-2 teaspoons of your filling of choice into the middle of each disk. Fold up the edges of the disk to form a triangle. Pinch the corners to “glue” them together. You may leave some the cookie open so the filling is visible, or you can choice to pinch the edges completely and create a “surprise” cookie.
Place the Hamantaschen, 2 inches apart, on a baking sheet covered with parchment paper, and bake for 12 minutes. The cookies should remain light colored. They are not supposed to brown too much.