Preheat oven to 375F. Line two baking sheets with parchment paper or very lightly spray with non-stick cooking spray; set aside.

Lay the two pieces of thawed puff pastry out flat on a clean work surface. Arrange 8 slices of ham on each piece of pastry so that it is mostly covered with the ham. Next, place 8 slices of cheese on each pastry over top of the ham.

Start at one end of the pastry and roll tightly into a log; repeat with the second pastry.

Use a sharp knife to cut the pastry logs into ¾-inch thick slices. Place each slice on the prepared baking sheets, leaving at least 1-inch between each.

In a small bowl, whisk together the egg and water. Lightly brush the egg wash over top of each pinwheel (discard the leftover egg wash). Sprinkle everything bagel seasoning onto the top of each pinwheel, if desired.

Bake the ham and cheese pinwheels at 375F for 18-22 minutes, until the pastry is puffy and turning golden brown around the edges. If your oven runs hot, start checking at the 15-minute mark. Cool slightly before serving.