Preheat the oven to 350 °F (175°C).
Warm butter in a frying pan over medium heat. Sauté the onion and garlic together for 5 minutes.
1 tablespoon butter, 1 medium onion, 2 cloves garlic
Remove the sausage from its casing and add to the pan also. Break apart into smaller pieces and brown all sides evenly, about 8 minutes.
1 pound chicken sausage
While the sausage browns, whisk 10 eggs in a large bowl. Mix in the cheese, thyme, salt, and pepper.
10 whole eggs, 1 cup cheddar cheese, ¼ cup Parmesan, ½ teaspoon dried thyme, ½ teaspoon salt, ½ teaspoon ground black pepper
Transfer meat to an 8x8-inch (20x20 cm) glass baking or casserole dish. Arrange in a single, even layer on the bottom.
Pour the egg mixture over the meat. Gently jiggle or tap the dish so the egg can settle down around the meat.
Bake for 20 minutes, until eggs are set and top is golden brown. Let rest 5 minutes before slicing and serving warm.