Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, until softened, about 5-7 minutes. Add the minced garlic, dried thyme, and rosemary and cook for another minute until fragrant.

Add the drained and rinsed cannellini beans, vegetable broth, and the bay leaf to the pot. Bring the mixture to a boil, then reduce the heat to low, cover, and let it simmer for 20 minutes to allow the flavors to meld.

Remove the bay leaf. Carefully transfer about 2 cups of the soup to a blender. Blend until completely smooth, then pour the puréed mixture back into the pot.

Stir in the coconut milk and bring the soup back to a gentle simmer. Cook for another 5 minutes. Remove from the heat and stir in the fresh lemon juice. Season with salt and pepper to your liking.