Heat the oil or water in a small skillet over medium heat. Add the garlic and cook until softened, about 1 minute. Remove from the heat and reserve.
Cook the penne in a large pot of salted boiling water, stirring occasionally, until it is al dente(about 8 minutes). About 5 minutes before pasta is done cooking, add the broccoli. drain the cooked pasta and broccoli well and return to pot.
While the pasta is cooking, combine the chickpeas and reserved garlic in a food processor. Add the broth, lemon juice, nutritional yeast, paprika, oregano, basil, pepper and salt to taste. Process until smooth.
Pour the sauce over the pasta and broccoli and toss gently to combine. Serve hot.