Minestrone with Green Beans and Fennel

Heat the oil and garlic in a medium saucepan over medium heat until the garlic begins to brown, 2 to 3 minutes; discard the garlic. Raise the heat to medium high, add the green beans, fennel, and 3/4 tsp. salt, and cook, stirring, until the beans and fennel begin to soften and brown in places, 5 to 7 minutes. Add the broth and the tomatoes with their juices and bring to a boil. Add the cannellini beans and pasta and return to a boil. Reduce the heat to a simmer, cover, and cook until the pasta and green beans are completely tender, 10 to 12 minutes. Stir in the cheese and basil and season to taste with salt and pepper. Serve sprinkled with additional cheese.