Preheat oven to 350 degrees.
Mix together the eggs, oil, sugar, and vanilla, beat until smooth and creamy. Sift together the flour, salt, and baking powder (honestly this makes all the difference in the dough). Add the dry ingredients to the sugar mixer, and blend together. This dough is a little sticky, you may need to add a bit more flour. Knead dough for about a minute before rolling out.
Roll out on a floured surface the thickness of the cookies should be about 1/4 of an inch, and using a round cookie cutter cut out circles. Place circles onto a parchment lined cookie sheet. You can fit about 12-15 cookies on each sheet. Fill with the filling of your choice. Fold into triangles, pinch together the corners. Brush the unbaked hamentashen with an egg wash which can be made using 1 egg and a tablespoon of water, beaten with a fork to combine.
Yield: 4 1/2 dozen
Bake in a 350 degree oven for 15-20 minutes until the cookies just begin to turn golden brown.