Heat a large pot or Dutch oven over medium heat. Add olive oil and butter. When butter is melted and foam subsides, add the diced onion, carrot, and celery. Sauté, stirring occasionally, until the vegetables are softened and the onion is translucent, about 6–8 minutes.

Add garlic and potato

Add the minced garlic and diced potato (if using). Cook, stirring, for 1–2 minutes until fragrant but not browned.

Liquids & Broth

Deglaze and add liquids

If using white wine, pour it in now to deglaze the pan, scraping up any browned bits from the bottom. Let the wine reduce by half (about 1–2 minutes). Add the chicken or vegetable stock and the water, stirring to combine.

Simmer

Add the bay leaf and thyme. Bring the pot to a gentle boil, then reduce heat to low and simmer, uncovered, until the vegetables are very tender, about 15–20 minutes. If you want a creamier finish, stir in the heavy cream or half-and-half during the last 5 minutes of simmering.

Seasoning & Herbs

Remove the bay leaf. Taste the soup and season with salt, freshly ground black pepper, and a pinch of red pepper flakes if using. Adjust seasoning gradually, tasting as you go.

Add-ins & Garnish

Finish with add-ins

If using canned tomatoes, add them after simmering and heat through for 3–4 minutes. Stir in cooked proteins or legumes to warm through (about 2–3 minutes). If you prefer a pureed or cream-style soup, use an immersion blender to partially or fully puree the soup to your desired texture—be careful with hot liquids.

Adjust and serve

Stir in chopped parsley and lemon juice, if using. Ladle into bowls and sprinkle with grated Parmesan if desired. Serve hot.