Preheat your oven to 400 degrees Fahrenheit (200 degrees Celsius). Line two baking sheets with parchment paper.
Unfold the thawed puff pastry sheets onto a lightly floured surface. Cut each sheet diagonally into 6 equal triangles, resulting in 12 triangles total.
Place one slice of ham and one slice of cheese near the wide end of each pastry triangle.
Starting at the wide end, roll each triangle toward the point. Gently curve the ends inward to form a crescent shape.
Place the rolled croissants seam-side down on the prepared baking sheets, spacing them a few inches apart.
In a small bowl, whisk together the beaten egg and 1 teaspoon of water to create an egg wash. Brush the tops of the croissants evenly with the egg wash.
Bake for 15 to 18 minutes, or until the croissants are puffed and golden brown.
Remove from the oven and let cool on the baking sheets for 5 minutes before serving warm.
Notes
For extra flavor, you can sprinkle a pinch of dried thyme over the cheese before rolling.
If you prefer a sharper taste, substitute sharp cheddar for Gruyère.
You can assemble these croissants up to 4 hours ahead of time; cover them loosely and refrigerate before brushing with egg wash and baking.