Bring a large pot of salted water to a boil. Once boiling, add the broccoli florets. Cook for 2 minutes. Remove with a slotted spoon and place the broccoli in an ice bath or run ice cold water over it to stop it from cooking.
Add the pasta to the same boiling water. Cook according to the directions. Once the pasta has finished, drain it from the pot. You can combine it and the broccoli in that same pot.
While the pasta is cooking, make the cheese sauce.
Melt the butter in a saucepan over medium heat. Once melted, whisk in the flour to create a roux. Whisk and cook until it’s golden and smelling nutty, about 2 minutes.
Mix the cream and milk in a measuring cup. Very slowly stream the mixture in, whisking the entire time. I steam it in about ¼ cup at a time, whisking the entire time, until it’s all incorporated. Continue to stir until the mixture thickens a bit. Stir in the cream cheese until it melts.
Turn off the heat. Add the cheese in small handfuls, stirring slowly and until completely melted. You’re going to add in about ¾ of the cheese - around 12 ounces. This will take awhile to stir and melt slowly. Don’t increase the heat because you want it to melt without getting grainy!
Taste the cheese sauce and season with a pinch of salt and pepper as needed. Pour the cheese sauce over the pasta and broccoli in the pot. Stir to combine. Once it’s all combined, I like to stir in the extra grated cheese as I serve it. This gives it an extra melty factor!