Combine the flour, parmesan, salt and pepper in a food processor and pulse a few times to combine. Add the butter and pulse until the dough comes together into a ball. Transfer to a work surface and shape into a ball. Cut in half and wrap each half in plastic wrap. Chill for 30 minutes.

Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.

Working with one piece of dough at a time, place on a well-floured work surface and roll out to about 1/4-inch thick. Using a 2-inch round cookie cutter, cut out the dough into circles and place on one of the prepared baking sheets, about 1/2-inch apart from each other. They don't spread out, so you can place them close together. Bring together the scraps, re-roll and cut out more circles. You'll want an even number of cookies since you'll be sandwiching them together. Using a smaller circle cutter cut out a hole in the center of half of the cookies. Set aside. Repeat with the second half of dough and place the cookies on the second prepared baking sheet.

Brush the tops with egg wash and sprinkle liberally with everything bagel seasoning. Bake until lightly golden brown, about 15 to 18 minutes, rotating the pans from top to bottom, front to back to ensure even baking. Remove from the oven and let cool completely on the baking sheets.

Transfer the cream cheese to a large piping bag, fitted with a plain circle tip, and pipe out about a tablespoon onto the bottom halves. Then place the top halves gently on top of the cream cheese. Serve immediately. Leftovers can be stored in an airtight container in the fridge for up to 3 days. Enjoy!