In a large heavy-bottomed pot over medium heat, add olive oil and butter. When butter has melted and begins to foam, add diced onion, carrot, and celery. Cook, stirring occasionally, until the onion is translucent and the carrots begin to soften, about 6–8 minutes. Add minced garlic and cook 30–45 seconds more until fragrant, taking care not to brown the garlic.

Vegetables & main components

Add hearty vegetables

Add the diced potatoes and zucchini to the pot and stir to coat with the aromatics. Cook for 2–3 minutes, stirring, to slightly soften the vegetables.

Add tomatoes and peas

Pour in the canned diced tomatoes with their juices and the frozen peas. Stir to combine.

Liquid & seasoning

Add liquid and seasonings

Add the vegetable or chicken broth and 1 cup water. Stir in the bay leaf, dried thyme, dried oregano, kosher salt, black pepper, and red pepper flakes if using. Increase heat to bring the mixture to a gentle boil.

Simmer

Once boiling, reduce heat to low, cover partially, and simmer until the potatoes are tender when pierced with a fork, about 15–20 minutes. Taste and adjust seasoning — add up to 0.5 tsp more salt if necessary. Remove and discard the bay leaf.

Finishing & garnish

Finish the soup

If you prefer a creamier texture, remove about 2 cups of the soup (liquid and solids) and purée in a blender until smooth, then return it to the pot and stir. Alternatively, for a lightly creamy soup, stir in heavy cream or half-and-half. Add fresh lemon juice and chopped parsley, stir to combine, and warm through 1–2 minutes without boiling.

Serve

Ladle the soup into bowls and sprinkle with grated Parmesan if using. Serve hot with crusty bread or crackers.