Preheat the oven to 375 degrees and grease a 9x13 baking dish. Cook and crumble the sausage in a large skillet, drain, then transfer to a large mixing bowl.
Add the onion, bell peppers, mushrooms, garlic, and kale to the mixing bowl with the sausage and toss to combine. Pour the vegetables into the greased baking dish.
In a large bowl (you can use the same one you just used for the sausage and vegetables), whisk together the eggs, Greek yogurt, milk, hot sauce, salt, and pepper.
Stir in 1 ½ cups of the cheddar cheese, then pour the egg mixture over the vegetables. Toss to coat the vegetables and sausage in the egg mixture.
Sprinkle the remaining ½ cup cheese over the casserole, then bake in the preheated oven for 40-45 minutes, until the cheese is melted and the eggs are cooked through. Serve!