Grating the carrots instead of finely dicing or chopping them will help your carrots cook quicker. I learned this tip for cooking an authentic Italian spaghettit bolognese from my friend's Italian Nonna. Optionally, I have seen other Italians cook spaghettit bolognese with by adding a glass of milk at the end. This gives a creamier texture to the Italian spaghetti bolognese sauce. The longer you cook your spaghetti bolognese, the better it will taste!