In a large pot, add oil and butter over medium heat.
Once butter is melted, add onions and carrots. Cook 7–9 minutes, stirring occasionally until they begin to turn golden. Season with 1/4 teaspoon each salt and pepper.
Stir in the minced garlic, tomato paste, and sugar. Continue to cook for another 1–2 minutes or until the tomato paste darkens in color.
Pour in the whole tomatoes with their juice, diced tomatoes, drained roasted red peppers, and chicken broth. Bring the mixture to a boil, then reduce the heat to a simmer. Let it simmer, uncovered, for 20 minutes, stirring occasionally.
Use an immersion blender to process the soup until it reaches a smooth consistency. Alternatively, carefully transfer the mixture to a blender (see note 2 for tips) and blend until smooth.
Return the pot to low heat and stir in the heavy cream. Season to taste (I usually add another 1/4 teaspoon each salt and pepper). If you choose not to add pesto, you’ll want some extra salt, pepper, and sugar. Add to taste.
Serve the soup warm with some hearty buttered bread or grilled cheese. Stir through a big spoonful (or to taste) of pesto into each bowl. Enjoy!
Notes
Note 1: Pesto packs a punch of flavor and seasoning, as well as a good amount of saltiness. If you skip it, remember to adjust the salt to taste!Note 2: When blending, blend in 3–4 batches. Securely close the lid. Use the “soup” or “hot” cycle if available. Be cautious of steam pressure; if no hot/soup setting, replace the lid with a towel and hold it securely. Carefully remove the lid to avoid steam bursts.Storage: Store this soup in an airtight container in the fridge for 3–5 days. Freeze in a freezer-safe container for 2–3 months.