Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery and cook for 5 minutes until they begin to soften.
Stir in 3 cloves of the minced garlic and cook for 1 minute. Add the diced tomatoes, vegetable broth, cannellini beans, zucchini, pasta, oregano, salt, and pepper. Bring the soup to a boil, then reduce the heat and simmer for 15 minutes until the pasta is tender.
While the soup simmers, mix the remaining 2 cloves of minced garlic with the softened butter and parsley. Spread the mixture on the baguette slices and place them on a baking sheet.
Bake the garlic bread at 400°F for 8 to 10 minutes until the edges turn golden. Stir the spinach into the soup during the last 2 minutes of cooking. Serve the soup in bowls with the warm garlic bread on the side.