In a large pot over medium heat, melt the butter and saute the diced onion until softened.
Add in the flour to the butter and onion. Stir continuously for 1-2 minutes. Make sure not to burn.
Whisk in the milk and stir until all of the clumps of flour have dissolved.
Bring the sauce to a simmer and stir until it thickens, about 5 minutes.
When the sauce is thick enough to coat the back of a spoon, turn the burner to low and add in the Velveeta cheese. Stir until all the cheese is melted.
Season the cheese sauce with salt and pepper to taste and stir in the cooked pasta. The sauce will thicken slightly more as it sits.
Add frozen broccoli to the boiling water for the last 2-3 minutes of the pasta cooking time.
Use any type of small pasta shape.
Add a teaspoon of hot sauce to the cheese mixture for an added "kick".