Preheat the oven: Preheat the oven to 350°F and grease a 9x13-inch baking dish with butter.
Brown the sausage: Cook the turkey sausage in a large skillet over medium heat, breaking it apart with a spoon, until no pink remains, about 6 minutes. Transfer to a plate and set aside.
Sauté the vegetables: In the same skillet, melt the butter and cook the onion and bell pepper until softened and fragrant, about 5 minutes.
Whisk the egg custard: In a large bowl, whisk the eggs, milk, salt, pepper, and paprika until smooth and evenly combined.
Layer the bread: Spread the cubed bread evenly across the bottom of the prepared baking dish.
Add sausage and vegetables: Scatter the cooked sausage and sautéed vegetables over the bread, then sprinkle with half of the shredded cheese.
Pour the custard: Pour the egg mixture evenly over the bread and toppings, pressing down gently with a spatula so the bread soaks it up.
Rest before baking: Let the dish sit for 10 minutes so the bread absorbs more of the custard, or cover and refrigerate overnight.
Top with cheese: Sprinkle the remaining shredded cheese evenly over the top of the casserole.
Bake until golden: Bake for 35 to 40 minutes, until the center is firm, the top is puffed, and the cheese turns golden brown at the edges.
Rest and serve: Let the casserole rest for 5 minutes before slicing into squares, so it holds together neatly.