Hamantaschen Dough. In a bowl, whisk together the flour, graham cracker crumbs (see Notes below), baking powder, and salt. Put aside.
In a mixer, cream the butter and sugar together for 2-3 minutes. Add the egg, the egg yolk, milk, and vanilla and beat until all the liquid ingredients are fully incorporated, approximately 2 minutes.
With the mixer off, pour the dry ingredients into the mixer bowl over the liquid ingredients. Turn the mixer on the lowest speed and mix just until the dry ingredients are fully incorporated. (Alternatively, you can mix the dry ingredients in by hand using a rubber spatula.) Do not overmix.
Place half the dough on top of a large piece of plastic wrap. Using the plastic wrap, shape the dough into a disk, pushing down on it to thin it out. Fully cover the disk of dough in the plastic wrap and place in the refrigerator for at least two hours and for as long as 24 hours. Repeat with the remaining portion of the dough.
Line 2 or 3 cookie sheets with parchment paper.
Brownie Filling. Place the marshmallows in a 2 quart saucepan over low heat. As they start to melt, stir them and add the butter and chocolate. Stir occasionally until all ingredients are fully melted. Remove from heat. Stir in the sugar and brown sugar. Set aside for a couple of minutes to make sure the mixture cools completely. Add the beaten egg and vanilla. Mix in the flour and salt just until all the flour is fully absorbed. Place batter into a piping bag or wrap in plastic wrap. Refrigerate the brownie batter for at least one hour.
Return to Hamantaschen Dough. Take one of the dough disks from the refrigerator and roll out in between two pieces of parchment paper. Roll the dough so that is approximately ¼ of an inch thick. If you roll it too thin, the dough will rip as you remove it from the parchment. Using a round cookie cutter (I use a 2½ inch diameter), cut as many rounds out as you can. You may need to dip your cutter into some flour to avoid it sticking to the dough. Use a metal spatula dipped in flour to release the rounds. Gather the scraps and roll that clump of dough out and cut more rounds. Keep repeating until you have used all the dough. If at any point the dough becomes too sticky or difficult to work with, cover it in plastic wrap and let it cool in the refrigerator for about 15 minutes.
Fill each round with approximately 1 teaspoon of the brownie filling. (It is easiest to fill the cookies by using a piping bag. If you do not have a piping bag.) Do not over fill them! Lightly flour your fingertips and form each circle into triangles by folding up the rounds and pinching them tightly in three corners. (If they are not sticking together, wet your fingertip and rub it on the inside where you are trying to create the point.) You want to make sure that the seams are fully closed so that the filling does not break through the barriers while baking. Place the shaped hamantaschen on the prepared cookie sheets.
Place the cookie sheets with the shaped hamantaschen in the freezer for 15 minutes. DO NOT SKIP THIS STEP.
Preheat oven to 400° F.
Repeat steps 7 through 9 with the remaining disk of dough.
Place one to three miniature marshmallows in the center of the brownie mixture. Bake the frozen hamantaschen for 9-10 minutes until they are lightly brown around the bottom edges.
Cool completely on pan or a wire rack before serving.