Bring a pot of salted water to a boil. Blanch the broccoli until tender. Then remove with a slotted spoon and set aside. (Use boiling water to cook the pasta, too.)
Cook the pasta according to the package instructions. Drain well.
Heat a nonstick pan on medium heat. Once hot, saute the hotdogs to golden brown on the outside.
Melt the butter in a saucepan over medium heat. Whisk in the flour and stir for about 1 minute until bubbly and golden brown.
Gradually whisk in the milk until smooth. Bring to a simmer while stirring occasionally. Once the sauce starts to thicken, add in the cheeses and whisk until smooth with no lumps. The sauce should be thick and creamy. Season with salt and pepper to taste. Mix in more cheese if needed.
Stir in the pasta until it is fully coated with the cheese sauce. Season with salt and pepper to taste before serving. Stir in the broccoli and hotdogs.