Position a rack in the center of the oven and preheat to 350 degrees F. Grease a 1 ½ quart baking dish or 9x9 baking dish with butter or cooking spray.

Whisk the eggs, milk, half-and-half, nutmeg, cayenne, 1 teaspoon salt, and ½ teaspoon pepper together in a large bowl.

Fold the greens, onion, meat, bread, and ½ cup of the shredded cheese into the mixture.

Pour into the prepared baking dish and top with the remaining cheese.

Cover with foil and bake for 35 minutes. Uncover and bake until the strata is puffed, golden brown at the edges and set in the center, about 15 minutes more.

Let rest for 5 minutes before serving.