Preheat oven to 400F. Grease a 9x13" baking with butter (and line the bottom with parchment paper if it's nonstick).
Combine the chopped bell peppers, onion, potatoes, olive oil, salt, black pepper, paprika, and dried oregano. Toss to combine, then roast for 20 minutes, until potatoes are fork tender.
Use your fingers to break up the ground beef (or breakfast sausage) into small pieces in the sheet pan. Season with ground cumin and brown sugar, then toss to combine all ingredients. Bake another 10 minutes.
Add the eggs and cottage cheese in a separate bowl. Whisk well. Pour over the meat and veggies mixture.
Use a spatula to evenly distribute all ingredients in the sheet pan. Top with the shredded cheddar cheese.
Bake until set in the center and crispy along the edges, about 15-20 minutes.