Preheat the oven to 375°F.
Heat the oil in a medium sauce pan over medium heat. Add the red pepper flakes, onion, garlic and carrots and stir to coat. Reduce the heat to low and cook for until everything is softened but not browned. Stir in the tomatoes and salt and bring to a gentle simmer, uncovered.
While the sauce is cooking, cook the pasta according to the package instructions. Brown the sausages. When the pasta is done, drain and put in a large bowl. Add the sausages, broccoli, cherry tomatoes, and sauce. Mix, taste and season with salt and pepper. Place in an oven-proof dish, top with cheddar and bake until cheese is melted and bubbly, 20 minutes or so. Enjoy hot with extra red pepper flakes to top.
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