Warm the pot: In a large soup pot, heat 2 tablespoons olive oil over medium heat. Add onion, leek, carrots, and celery with a pinch of salt. Cook 5–7 minutes, stirring, until softened and glossy.

Build the base: Stir in potatoes, bay leaf, thyme, and the Parmesan rind if using. Pour in the vegetable broth. Bring to a gentle boil, then reduce to a simmer. Cook 10–12 minutes, until potatoes are almost tender.

Add green vegetables: Add zucchini and green beans. Simmer 5 minutes. Then add asparagus and peas, and cook 3–4 minutes more, until crisp-tender and vibrant.

Stir in beans: Add the cannellini beans and warm through for 2–3 minutes. Taste and season with salt and pepper. Remove bay leaf, thyme sprigs, and Parmesan rind.

Make the pistou: While the soup simmers, combine basil, garlic, cheese (if using), lemon zest, and a pinch of salt in a food processor. Pulse to chop. With the motor running, stream in 1/3 cup olive oil until you have a loose, spoonable paste. Adjust with more oil, salt, or pepper to taste.

Finish the soup: Off the heat, stir in 2–3 tablespoons of pistou to the pot to perfume the broth. Ladle soup into bowls and top each with another spoonful of pistou for a bright finish.

Serve: Add a squeeze of lemon if you like, more cheese, and a drizzle of olive oil. Serve with warm crusty bread.