In a large mixing bowl, whisk the cream cheese and butter until fluffy. Add the flour, sugar and salt and stir until combine. Add the egg and combine until a dough has formed. Wrap dough in plastic wrap and refrigerate at least 2 hours, preferably overnight.
When ready to bake the hamantaschen, preheat the oven to 375 degrees F. and line two baking sheets with parchment paper.
Sprinkle flour on your work surface and roll out the dough to around 1/8 inch thick. Cut 2-3 inch rounds with a cookie cutter or the top of a glass cup. Place the rounds on the baking sheets. Roll out the scraps and continue cutting out rounds of dough.
Filling and Topping
Slice the jalapenos into one-inch rounds and remove the seeds.
In a a small mixing bowl, blend together the cream cheese and cheddar cheese and transfer it to a piping bag or large ziploc bag. Cut off the tip of the bag.
Separately, stir together the bread crumbs, paprika, garlic powder, salt and olive oil.
Assembly
Press a sliced jalapeno into the center of each dough round. Brush the edges of the dough with water or a whisked egg (both will help the dough stick together) and press the dough together to create a triangle. Fill the jalapeno with the cream cheese/cheddar mixture then sprinkle with the bread crumbs.
Bake the hamantaschen for 10-12 minutes, until the edges of the dough are beginning to brown.
Eat hot or at room temperature. Really, there is no wrong way to eat these jalapeno popper hamantaschen. Store in an airtight container in the refrigerator for 3-4 days or freeze for up to 3 months.