Place the roasted tomatoes, peppers, broccoli florets, onion, garlic, and carrots into a food processor. Pulse until a 'smoothish' consistency is reached, leaving some texture for a rustic feel.

Transfer the processed mixture to a large pot. Bring to a boil, then reduce heat to low and simmer until the sauce reaches your desired thickness.

During the last 10 minutes of simmering, stir in fresh herbs (parsley, basil, oregano), salt, and pepper to taste.

If the sauce is too acidic, add a small pinch of sugar to balance the flavors. Continue simmering for a few more minutes to blend the flavors.