Heat a large heavy-bottomed pot or Dutch oven over medium heat. Add olive oil and butter. When butter melts and starts to foam, add the chopped onion, carrot and celery. Cook, stirring occasionally, until softened and translucent, about 6–8 minutes.

Add garlic and flour

Add the minced garlic and cook 30–45 seconds until fragrant. Sprinkle the tablespoon of flour over the vegetables and stir to coat; cook 1 minute to remove the raw flour taste.

Deglaze

If using, pour in the white wine to deglaze the pot, scraping any browned bits from the bottom. Let the wine reduce for 1–2 minutes.

Add stock and herbs

Add the chicken or vegetable stock, bay leaf, dried thyme, salt, and pepper. Bring to a gentle simmer.

Vegetables & Add-ins

Cook root vegetables

Add the diced potato to the simmering broth first because it takes longest to cook. Simmer for 8–10 minutes until the potato begins to soften.

Add remaining vegetables

Add diced zucchini, canned diced tomatoes with their juices, and the Parmesan rind if using. Continue simmering 6–8 minutes until zucchini is tender.

Add beans and peas

Stir in the drained cannellini beans and frozen peas. Simmer 3–4 minutes until heated through.

Wilt the greens

Add the chopped spinach or kale and cook 2–3 minutes until wilted and bright green. Remove and discard the bay leaf and Parmesan rind (if used).

Finishing & Garnish

Adjust seasoning and finish

Stir in the lemon juice, chopped parsley, grated Parmesan, and red pepper flakes. Taste and adjust salt and pepper to taste. If the soup is too thin, simmer uncovered 5–10 minutes to concentrate flavors; if too thick, add up to 1 cup extra stock or water.

Serve

Ladle the soup into bowls and garnish with an extra sprinkle of Parmesan and parsley. Serve with crusty bread if desired.