Cook pasta according to box directions adding the broccoli 2 minutes before pasta cook time ends, drain and set aside.
In a medium saucepan melt the butter over medium heat and add the flour, salt, and pepper. Stir until combined, about 1 minute.
Turn heat to medium-high and slowly whisk in the milk and keep whisking until mixture comes to a boil.
Reduce heat to low and simmer stirring occasionally until mixture becomes thick like heavy cream.
Take off the heat and stir in the cheeses until melted and fully incorporated.
Add the pasta and broccoli, stir to combine, add salt and pepper to taste.
