Pluck the outer leaves of the puntarelle, wash, chop into large pieces and set aside. Divide the finger-length pieces of the puntarelle, cut off the lower (woody) end and cut the thicker pieces in half. Clean the carrots, quarter them and cut into 3-4 cm long pieces. Clean the peppers, remove the seeds and cut into bite-sized pieces. Peel the garlic and cut into thin slices.
Heat the oil in a pan and fry the carrots vigorously. Add the puntarelle, bell pepper pieces and garlic and also fry over a high heat. The vegetables should get color, but still have a good bite.
Remove from the plate and season with salt, pepper and chilli to taste.
Mix in the chopped puntarelle leaves, place again briefly on the hot plate and toss.
Spread the roasted vegetables on plates, sprinkle with parmesan and serve with white bread or mashed potatoes.