Begin by washing and chopping your vegetables: dice the potatoes, zucchini, carrots, and celery into uniform pieces, and slice the leek and onion. Set them aside in bowls.

In a large, heavy-bottomed pot, heat 2 tablespoons of frying oil over medium-low heat. Add the chopped onion and sliced leek, stirring occasionally for about 8 minutes until they become soft and translucent.

Add the remaining tablespoon of oil to the pot and toss in the diced zucchini, potatoes, carrots, and celery. Allow the vegetables to cook undisturbed for the first minute, then stir to combine and coat them in the oil. Cook for an additional 5-7 minutes until they start to soften.

Return the sautéed onions and leeks to the pot and pour in 8 cups of water. Cover the pot to come to a gentle boil, then reduce the heat to low and let it simmer for about 15 minutes.

Add your handful of green beans into the pot. Bring the soup back to a boil, then incorporate the green peas and rinsed cannellini beans. Cook for an additional 2 minutes until the peas are heated through.

Remove the pot from heat and season your soup with salt and pepper to taste. Let the soup sit for a minute to settle the flavors.

In a blender, combine 4 cups of fresh basil leaves, 2 cloves of garlic, 1/3 cup of grated Parmesan cheese, and a pinch of salt. Blend until smooth, then drizzle in 3 tablespoons of olive oil while blending.

Ladle your hearty French vegetable soup into bowls and stir in cooked small elbow pasta, if desired. Top each serving with a spoonful of pistou just before eating.