In a large stand mixer (or hand mixer), cream the butter until light and soft. Add sugar and cream together.
Add 1 egg, vanilla and orange zest and mix well.
In another bowl, sift together the flour and salt.
In about 2 batches and with the mixer on low speed, slowly add the flour mixture. Mix until just combined and use a spatula to scrape down the sides making sure everything is incorporated well.
Once mixed, take dough out and knead on a lightly floured surface until a smooth ball forms. Form the dough into a round, flat disk and wrap in plastic wrap and place in refrigerator for about 30 minutes or freezer for 10-15 minutes.
Remove dough from freezer or refrigerator and flour surface very well. Begin to roll out the dough and if the dough is too hard to roll, let it rest on the counter and pound with a rolling pin, if needed. This will help the dough create flexibility to roll out.
Roll out dough to about ¼ inch thick and use a 3 inch round cookie cutter to cut out circles. Don't discard scraps, knead and roll out again to cut more circles.
Take one circle and place a teaspoon of filling in the center. Take one side of circle and fold in. Take other side and fold in, bringing the top corners together.
Pinch the corners and place the hamantaschen on a lined baking sheet. Whisk the other egg with a bit of water and brush egg wash onto hamantaschen cookies.
Bake the cookies at 350 degrees Fahrenheit for about 22-25 minutes, rotating the pan halfway through.
Let the cookies cool on baking sheet for about 5 minutes before transferring to a cooling rack and serving.