Cook the pasta in plenty of salted water until cooked.
Put the oil in a pan and sauté the diced onions and carrots in it for a few minutes. Then add the diced ham. After a few minutes add the milk and cream and stir the tomato paste into the sauce. Let simmer for a few minutes. Season well with salt, pepper, garlic and a pinch of sugar.
If the sauce is too runny: Mix 1 tablespoon of cornstarch with water and stir slowly in the simmering sauce until the desired consistency is achieved.
Divide the pasta on plates and pour the sauce over the pasta.