Combine chicken broth, half and half, chicken bouillon cube, hot sauce, onion powder, garlic powder, oregano, basil, mustard powder, and parsley in a large measuring cup. Stir well and set aside.
Cook Gemelli pasta in salted boiling water until al dente, about 8-10 minutes. Drain and set aside.
Melt butter in a skillet over medium heat. Whisk in flour and cook 1-2 minutes to form a roux without browning.
Gradually whisk the broth mixture into the roux, stirring constantly to avoid lumps. Add finely chopped broccoli, bring to a gentle boil, then simmer until slightly thickened.
Lower heat and gradually add shredded cheddar cheese, stirring until melted and smooth. Add cooked pasta and toss until evenly coated.
Serve warm with a sprinkle of grated Parmesan cheese on top.
Notes
This cheese pasta is highly adaptable—feel free to swap cheeses or add extra vegetables or protein to make it your own.