Bring a large pot of water to a boil and add the spiral pasta. Cook the pasta to al dente according to the package directions. Then, add the broccoli florets and boil them with the pasta for the last minute of cooking time. The florets will be bright green and tender but still have a little bite. Scoop out 1 cup pasta water and set it aside. Drain the broccoli and pasta in a colander; hold on to these for later. Editor's Tip: Remember to salt the pasta water after it's come to a rolling boil but before you add the pasta to the pot.
Dry the pot and add the butter, melting it over medium heat. Once it's melted, add the minced garlic. Stir and saute the garlic for 30 seconds to one minute or until fragrant. Then, stir in the flour for another minute or two until the butter, flour and garlic form a thick paste.
Add the chicken broth, salt, onion powder, paprika and pepper to the pot. Slowly stir in the warmed half-and-half cream. Stir everything together and bring the mixture to a low simmer. Continue stirring. As soon as the sauce begins to look thickened—which should take three to four minutes—remove the pan from the heat.
After you've removed the pot from the heat, stir the shredded cheddar and Parmesan cheeses into the sauce. Continue stirring until they're melted and the sauce is smooth.
Add the cooked pasta and broccoli to the pot. Toss everything together until the pasta is thoroughly coated in cheese sauce. If necessary, add a splash of the pasta water to the pot to help loosen the sauce and make it creamy. Serve the cheddar broccoli pasta while it's hot.
