Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease.
Beat eggs and milk together in a large bowl. Stir sausage, Cheddar cheese, spinach, and oregano into egg mixture; pour into prepared baking dish.
Bake in the preheated oven until a knife inserted into the center of the casserole comes out clean, 30 to 40 minutes.