Preheat your oven to 300F and line two baking sheets with parchment paper.
In a clean bowl, whip the egg whites with a hand mixer until stiff peaks form, about 3 to 4 minutes.
In a separate bowl, toss together the shredded sharp cheddar cheese, grated parmesan cheese, garlic powder, smoked paprika, onion powder, and salt until well combined.
Gently fold the cheese mixture into the whipped egg whites using a spatula. Work carefully to keep as much air in the mixture as possible, folding just until the cheese is evenly distributed.
Drop rounded teaspoon-sized mounds onto the prepared baking sheets, spacing them about 1 inch apart. You should get about 30 puffs.
Bake for 22 to 25 minutes until the puffs are golden, dry to the touch, and feel light when you pick one up. Let them cool completely on the pan. They will become airy and crunchy as they cool.