In a large heavy-bottomed pot, heat 2 tablespoons of olive oil over medium heat. Add the sliced leeks, celery, and garlic, cooking for about 5 minutes until softened and fragrant.

Stir in the diced potatoes, thyme, herbs de Provence, salt, and pepper, allowing the mixture to sauté for another 10 minutes until the vegetables are tender and lightly translucent.

Increase the heat slightly and add ½ cup of white wine to the pot. Stir vigorously, scraping the bottom to release any caramelized bits, and let it cook for 3-4 minutes until the wine nearly evaporates.

Pour in 5 cups of vegetable broth and add the drained cannellini beans to the pot. Bring to a gentle boil, then simmer uncovered for 10-12 minutes, stirring occasionally until the potatoes are fork-tender.

Using a spoon, mash a portion of the potatoes and beans against the side of the pot to thicken the soup. Alternatively, use a hand blender for a smoother texture.

Stir in 2 cups of fresh spinach and 2 tablespoons of lemon juice, mixing until the spinach wilts, about 2 minutes.

In a blender, combine 1-2 cloves of garlic, ½ teaspoon of sea salt, and 2 cups of fresh basil leaves. Blend while slowly drizzling in ⅓ cup of olive oil until a smooth paste forms.

Ladle the warm soup into bowls and top each serving with a generous dollop of the prepared pistou.