Place cauliflower into a large pot and cover with water; bring to a boil. Reduce heat to medium-low and simmer until tender, 7 to 10 minutes. Drain.

Mash cauliflower in a bowl until smooth. Beat Cheddar cheese, Parmesan cheese, eggs, cayenne pepper, and salt into cauliflower.

Melt butter in a skillet over medium-high heat. Pour cauliflower mixture into hot butter and cook until golden, about 5 minutes. Flip cauliflower mixture; cook and stir until mixture is more crumbly than creamy, about 10 minutes more.