Prepare the tomatoes: Wash, core, and quarter your heirloom tomatoes. For a smooth soup, remove the skins and seeds later with a food mill.
Chop the vegetables: Dice the bell pepper (discarding the stem, seeds, and membranes) and peel and chop the onion.
Cook the soup base: Heat the olive oil in a large stock pot or Dutch oven. Add the chopped onion and minced garlic, sautéing until the onions are translucent but not browned.
Simmer the soup: Add the prepared tomatoes, bell pepper, sugar, salt, and pepper to the pot. Bring everything to a boil, then lower the heat and let it simmer, uncovered, for about 30 minutes. You want the tomatoes to soften and the mixture to thicken slightly.
Strain the soup: To remove the skins and seeds, use a food mill or food strainer. This will give you a smooth, velvety texture. Popular options include the Kitchenaid food strainer attachment, a Victorio manual food strainer, or a rotary food mill.
Simmer again: Once the soup is strained, return it to the pot and simmer for another 25 to 40 minutes to thicken it further. The total time will depend on how watery your heirlooms were at the start. You’re going for soup thickness, so stop before you reach a tomato sauce consistency.