First, prepare the dough. Combine the cream cheese and butter in a large mixing bowl and beat them together well with a hand mixer. Slowly add the flour in while you continue to beat the batter until it forms a soft, sticky dough. Bring the dough together into a ball in the bowl with clean hands, then cover it. Let it chill in the refrigerator for three hours. When the three hours are up, pre-heat the oven to 350 and line 2 sheet trays with silicone mats.
Take the dough and divide it into quarters. Dust a clean work surface with a little flour and powdered sugar and roll the first quarter out until it is 1/8 inch thick. Use a 1 1/2 to 2 inch square cutter, depending on how big you want them, and cut out perfect little squares out of the rolled out dough. Be sure to cut them out as close together as possible to minimize scraps. Take the scraps and roll them out again to cut out as many more squares as possible. Lay the squares out on one of the sheet trays.
Scoop 1/2 a teaspoon of the apricot filling into the center of the first square. Then bring two of the opposite corners together and pinch them together well. It will look like a tiny cannoli. Repeat that until all of the squares are filled and formed into the kiffles. Then repeat the process with the next quarter of dough, but use the cherry filling for the second tray. Brush all of the kiffles with the egg wash to help seal them and make them golden, then bake them for 10-12 minutes. They should be golden.
When they are done, take them out and let them cool for 5 minutes before transferring them to cooling racks to finish cooling. While they are still warm, dust them with more powdered sugar. Repeat the whole process with the last half of the dough, making a tray of apricot and a tray of cherry. When they are all completely cooled, store them in sealed tins where they will keep for weeks in a cool place. Enjoy giving them out and eating them for the Holidays!