Heat the oil in a medium pot, then add the onion & carrot. Fry over medium-high heat until soft but not brown yet.
Add the garlic and fry for another minute. Add the mince and mushrooms and fry, breaking up lumps with your wooden spoon. Fry until the mixture starts to catch on the bottom – about 10-15 minutes, then add the tomatoes, stock, sugar, paprika and stir well.
Season with salt & pepper, then cover and simmer over low heat for at least 30 minutes (or up to 2 hours), stirring now and then.
Taste and adjust seasoning if needed. Serve hot over freshly cooked pasta, scattered with fresh basil and Parmesan cheese.