Position a rack in the center of the oven and preheat to 350 degrees F. Grease a 1 1/2 quart baking dish with butter or cooking spray.
Whisk the eggs, milk, half-and-half, nutmeg, cayenne, 1 teaspoon salt and 1/2 teaspoon pepper together in a large bowl. Fold the greens, meat, bread and 1/2 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 cool 10 minutes before serving.
This strata can be baked immeditately or assembled the night before and refrigerated until baking the following morning. After removing it from the refrigerator, let the assembled strata stand at room temperature 15 to 20 minutes before baking.
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