Cook noodles in a pot of generously salted water to al dente according to package instructions.
During the last few minutes of the noodles cooking, add the broccoli florets to the pot. Drain noodles and broccoli together.
Prepare the cheese sauce while the noodles (and broccoli) are cooking.
Melt butter in a large skillet over medium low heat. Add flour and whisk together for a minute or two. Gradually pour milk into the skillet while whisking constantly to prevent lumps in the sauce. Once combined, increase heat to medium high and bring sauce to a gentle boil to thicken, stirring often.
Add salt and pepper, mustard powder and paprika. Once sauce is thickened, stir in cheddar cheese and parmesan cheese.
Add drained noodles and broccoli, and chicken to the skillet and stir to combine it with the cheese sauce.
Serve immediately.
Alternately, pour into a greased casserole dish and cover with foil. Store in the fridge for up to several days and warm in a 350°F oven for 30-40 minutes until heated through.