Place a large pot of water over high heat to boil. Once boiling, salt the water and drop the pasta in. Cook to al dente according to package directions. Drain cooked pasta and reserve.
While the pasta is working, place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the ground sirloin and cook until golden brown, 6-7 minutes.
Add the onion, garlic and carrots to the pan and cook until tender, 4-5 minutes. Add the tomatoes, basil, salt and pepper to the pan and break up the tomatoes into a chunky sauce using a potato masher or the back of a spoon. Bring the liquid to a bubble and simmer just until slightly thickened, about 5 minutes.
Add the reserved tortellini to the skillet and toss to coat with the sauce. Transfer to a large casserole dish and sprinkle with the cheeses. Place under the broiler to brown, about a minute.