Bring a large pot of salted water to a rolling boil. Add your chosen pasta and cook according to package directions until al dente.
About 3–4 minutes before the pasta is done cooking, add the broccoli florets to the boiling pasta water.
Once your pasta is al dente and broccoli is tender-crisp, reserve about 1 cup of that starchy pasta water and drain both.
In a large skillet over medium heat, melt unsalted butter. Add chopped onion and sauté for about 5–7 minutes until softened. Then add minced garlic and smoked paprika, cooking for another minute.
Sprinkle flour over the sautéed onions and garlic. Whisk constantly for about 1–2 minutes to cook out the raw flour taste.
Gradually whisk in vegetable broth little by little, then whisk in milk gradually as well.
Bring your sauce to a gentle simmer while stirring frequently for about 3–5 minutes until it thickens.
Stir in Dijon mustard and season with salt and pepper as desired.
Reduce heat to low and add grated cheddar cheese gradually, stirring until melted. If using cream cheese, stir it in until smooth.
Add cooked pasta and broccoli into your cheese sauce and stir until evenly coated. Adjust with reserved pasta water if too thick.
Serve immediately with fresh chopped parsley and a sprinkle of black pepper.