Add olive oil and garlic to a medium-sized pot over medium-high heat. Add in flour, whisking until a paste forms. Add in broth, milk, salt and pepper and bring to a boil. Lower heat and bring to a simmer.
Add parmesan cheese, whisking well to combine. Add Chickapea Pasta spirals and stir well to coat, letting simmer for 4-5 minutes or so until pasta is tender. Stir in broccoli and cook another 2 minutes until broccoli is tender and sauce is mostly absorbed.
Serve with extra parmesan cheese on top and enjoy!