In a large pot, melt butter. Add onion and cook on low about 6 minutes, until onions are soft.
Add flour and stir, cooking another minute.
Add chicken broth, celery, carrots, garlic, bay leaves and salt and pepper to taste. Add chicken and bring to a boil, then partially cover, simmer on low 30 minutes.
Meanwhile, cook cavatelli in a pot of salted water according to package directions.
Drain and add to soup when soup has cooked. Cook another minute or two.