1. Bring a pot of generously salted water to a boil. Boil the pasta 2 minutes less than the package directions (because it will finish cooking in the sauce), then drain.
2. Meanwhile, in a pot preheated over medium heat, melt the butter and then add the flour. Cook the flour while whisking constantly for 1 minute, then start gradually adding the milk 1 cup at a time, whisking so that the milk gets fully incorporated before adding more.
3. Once all of the milk is added, turn the heat up to medium high and continue whisking until the white sauce starts to bubble and thickens enough to coat the back of a spoon (3-5 mins). Add the kosher salt, pepper, cayenne, mustard powder, garlic powder, and paprika.
4. Add the broccoli and cook for 3-5 minutes, stirring often, until the broccoli is almost tender. Add the pasta and cheddar cheese and cook for about 2 more minutes, stirring often, until the pasta is your desired tenderness. Enjoy!
