Place the minced beef or lamb and onion in a large pan and fry with the chopped onions until the meat has browned all over. There's no need for oil as there's enough fat in the mince. You may like to drain off some of the fat when the meat is cooked.
Add carrots to the meat, and sprinkle over the flour. Cook for a further 2 or 3 minutes until the flour has been absorbed, then add the tomatoes. Season to taste. Simmer the mince for 30 minutes.
Meanwhile, bring a large pan of lightly salted water to the boil, and cook the penne until al dente, which should be about 10 minutes. Drain and place in an oven proof dish, keeping warm. Pour the Bolognese sauce over the top of the penne, stirring it into the pasta. Sprinkle over the grated cheese and grill until hot and bubbling.
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home.