1. Preheat the oven to 375 degrees F and spray a 9 x 13-inch baking dish with cooking spray. Set aside.
2. Heat a skillet over medium-high heat, add half of the olive oil and the breakfast beef sausage. Cook for about 5 minutes, stirring frequently, until the sausage is golden brown. Transfer the cooked sausage to the prepared baking dish.
3. Return the skillet to the stove and add the remaining olive oil. Add the chopped onion, both bell peppers, 1/4 teaspoon salt, and 1/2 teaspoon ground black pepper. Sauté for about 5 minutes, stirring occasionally, until the vegetables are slightly browned. Transfer the vegetables to the baking dish with the sausage, spreading everything out in an even layer.
4. In a large mixing bowl, whisk together the eggs, cottage cheese, milk, 1/2 cup shredded cheddar cheese, and 1/4 teaspoon salt. Pour this mixture evenly over the sausage and vegetables in the baking dish. Gently stir the mixture with a spoon so the peppers rise to the top and create some color.
5. Sprinkle the remaining 1/4 cup cheddar cheese over the top.
6. Bake uncovered for 40 minutes. Remove from the oven and let cool for 20 minutes before slicing.
7. Cut into 10 slices and serve warm or cold.