Bring a large pot of water to boil over high heat. When the water is at a rolling boil, add some salt and then add the pasta shells.
Cook the pasta shells for 5 minutes and then add the broccoli florets to the water as well. Cook both, together, for another three minutes and then drain in a colander.
Add 1 tbsp of butter to the shells and pasta while in the colander so they don‘t stick together.
To the large empty pot, add 3 tbsp of butter over medium heat and melt. Next add 3 tbsp of flour, whisking constantly so that there are no lumps. Cook the flour for 2 minutes, whisking constantly.
Slowly add the milk, whisking constantly until all the milk is added and smooth (no lumps). Let the milk cook for a few minutes until it has thickened. Add the salt, pepper, garlic powder, and dried mustard. Stir.
Add 2 cups of the cheese and stir until it has melted. Add the shells and broccoli back the pot and stir until they are coated. Remove from heat.
Add in the remaining 1/2 cup of cheese and stir. Serve warm. Enjoy!