In a large heavy-bottomed pot or Dutch oven, heat the olive oil and butter over medium heat until butter melts and foams. Add the diced onion, carrot and celery. Cook, stirring occasionally, until the vegetables are softened and the onion is translucent, about 6-8 minutes.

Add the minced garlic and cook for 30-45 seconds until fragrant, taking care not to brown it.

Sprinkle the flour over the vegetables and stir for 1-2 minutes to cook the raw flour taste, forming a light roux that will slightly thicken the soup.

Slowly pour in the vegetable (or chicken) stock while stirring or whisking to avoid lumps. Add the water, bay leaf, thyme sprigs, salt and pepper. Bring the mixture to a gentle simmer.

Main Additions (seasonal vegetables / protein)

Add the diced potato and butternut squash/pumpkin to the simmering broth. Partially cover the pot and simmer gently until the vegetables are tender when pierced with a fork, about 15-20 minutes.

When the vegetables are nearly done (with 5 minutes remaining), add the green beans and canned white beans (if using) so they heat through but remain slightly firm. Taste and adjust seasoning with additional salt and pepper as needed.

If you prefer a fully smooth soup, remove the bay leaf and thyme sprigs and blend using an immersion blender until smooth and velvety. For a chunky soup, skip blending and leave vegetables as-is. If blending, return to low heat after blending.

Finishing & Garnish

Stir in the heavy cream or coconut milk, if using, and warm through for 2-3 minutes without boiling. Add the lemon juice to brighten the flavor.

Remove from heat. Taste and adjust seasoning. Stir in half of the chopped parsley and half of the grated Parmesan (if using).

Ladle soup into bowls. Garnish each bowl with remaining parsley and a sprinkle of Parmesan. Serve with crusty bread on the side.