Preheat oven to 425F.
Cut the end off the heads of garlic, drizzle with EVOO and season with salt and pepper. Wrap them in foil and roast to soft, 40-45 minutes.
Reduce heat to 300F. Arrange halved tomatoes on a cooking rack set on a baking sheet so heat can circulate around the tomatoes. Drizzle with EVOO and season with salt, pepper and herbs of choice. Roast 2 hours.
When tomatoes are done, sauté onions in EVOO, a turn of the pan, until soft, 10 minutes. Place roasted garlic cloves, half the roasted tomatoes, onions and canned tomatoes in a food processor, and pure until smooth. Place tomato base in a pot with the stock and stir to combine and heat through.
Chop remaining roasted tomatoes then stir into soup to give the soup some texture. Serve in shallow bowls topped with basil and cheese puffs or grilled cheese sandwiches alongside.