Step 1

Heat 3 tablespoons of olive oil in a large saucepan over medium-high heat. Add the onion and 3 cloves of garlic and cook, stirring occasionally, until softened, about 4 minutes.

Step 2

Add broccoli florets and stems, beans, broth, water, salt and pepper. Bring the mixture to a boil, then reduce heat and simmer until the broccoli is tender, 18 to 20 minutes. Let cool for 5 minutes.

Step 3

Transfer the soup to a blender. Add vinegar and purée until smooth. Return the mixture to the saucepan over low heat. Slowly add the cheese, stirring after each addition, until melted, 1 to 2 minutes.

Step 4

Heat the remaining 5 tablespoons of olive oil in a large skillet over medium-high heat. Add the baguette slices and cook, flipping once, until golden brown on each side, about 4 minutes. While they’re still warm, rub each slice of bread with the remaining garlic clove. To serve, divide the soup among 4 to 6 bowls and top with the remaining cheese and another crack of black pepper, then serve with toasts for dipping.