Preheat oven to 400°F. Halve the tomatoes lengthwise and arrange on a large (15x21-inch) sheet pan (or two smaller sheet pans). Quarter the onions and add to the pan(s).
Peel the outer layers of the garlic bulb, leaving the clove skins intact. Cut off 1/4 inch from the top of the cloves, drizzle with 2 teaspoons olive oil, wrap tightly in foil, and place on the sheet pan with the tomatoes and onions.
Drizzle 1/4 cup olive oil over the tomatoes and onions, sprinkle with 1 teaspoon salt and 1/2 teaspoon pepper, toss to coat, and spread in an even layer. Roast 40–45 minutes until tender and slightly caramelized.
In a large stockpot or cast iron pot, heat butter and 2 tablespoons olive oil over medium heat until butter melts. Add can of tomatoes and tomato paste, stirring 2–3 minutes. Mix in chicken stock, oregano, optional red pepper flakes, thyme, and fresh basil. Incorporate roasted tomatoes and onions with all their juices. Let garlic cool slightly, then squeeze out the cloves from their skins and add 6–9 cloves to the soup, depending on your taste. Season with 2 teaspoons salt and 1 teaspoon pepper, or adjust to taste.
Bring mixture to a boil, then reduce heat to low and simmer uncovered 40 minutes, stirring every 5–10 minutes.
Transfer the mixture in 3–4 batches to a high-powered blender and blend until smooth (see note 2). Taste and adjust seasonings as needed. If tomatoes are too acidic, add a teaspoon of granulated sugar.
If desired, serve with freshly grated Parmesan cheese and hearty buttered bread. Enjoy!
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Notes
Note 1: If buying the packets of basil, this comes out to 4 packets (3/4 ounce each).Note 2: Secure the blender lid tightly and use the “soup” or “hot” cycle. Increase speed gradually to prevent overflow due to heat expansion and carefully remove the lid to release steam. If your blender lacks this setting, cover it with a folded towel for safety. For a chunkier soup, use an immersion blender, chopping the roasted onions and garlic coarsely before adding them to the pot.Storage: This soup stores nicely in the fridge an airtight container up to 4–6 days. It freezes well for up to 3 months. Here are some best methods for thawing frozen soup.