Heat the olive oil in a large skillet over medium heat, and cook and stir the carrots, onion, and garlic until tender, about 10 minutes. Place the ground beef into the skillet and cook and stir, breaking up the meat as it cooks, until browned. Drain off excess fat from the skillet, and pour in 1 cup milk. Bring to a simmer, reduce heat to medium-low, and simmer until the milk is absorbed, about 15 minutes.
Place the beef mixture into a slow cooker, and set the cooker toHigh. Stir in crushed tomatoes, tomato paste, salt, pepper, basil, oregano, and red pepper flakes, and cook for 2 hours. Mix in 1/2 cup milk and Parmesan cheese, stir well, and cook for 2 more hours.
