Cook and stir beef, salt, and black pepper in the hot skillet on medium high heat until browned and crumbly. Drain and discard grease. Add onion, carrot, and garlic to ground beef; cook and stir until onion is lightly browned, about 15 minutes.
Mix tomatoes, tomato sauce, mushrooms, brown sugar, and Worcestershire sauce into ground beef-vegetable mixture. Season with salt and black pepper. Cook on low until liquid is reduced and flavors have blended, about 45 minutes.
Bring a large pot of lightly salted water to a boil. Cook the penne pasta according to package. Transfer drained and cooked pasta to a 9×13-inch casserole dish.
Spoon cream of mushroom soup over pasta; top with ground beef-tomato mixture. Add Cheddar cheese on top.
Bake in the preheated oven until casserole is bubbling and Cheddar cheese is melted, about 45 minutes.