Add oil to 4-quart pot and heat until shimmering. Chop onion. Add onion and pressed garlic to pot and cook 1-3 minutes until tender.
Add broth, pasta, salt and black pepper to pot; bring to a boil. Meanwhile, cut green beans and zucchini into 1/2" pieces. Reduce heat to medium; add vegetables and cannellini beans. Cook 8-10 minutes or until pasta is tender. Grate cheese and snip parsley.
Ladle soup into serving bowls. Top with pesto, cheese and parsely.