Create a roux by warming and melting the two tablespoons of butter in a large skillet and adding one tablespoon of flour. Whisk well until all of the flour is incorporated. If you like your sauce on the thicker side, use 2 tablespoons of flour.
Slowly add in 1 cup of milk. While whisking to combine, bring the mixture to a low simmer over a medium heat. Do not boil. Once it is simmering, cook for 2 minutes.
Why the mixture is coming up to a simmer, bring a sauce pot filled with water to a boil. Add the sea salt, minus a pinch or two.
Add the broccoli and cook for 1 minute, just until it turns a brighter green. It will be on the crunchy side, cook for 2 minutes longer for a more tender broccoli.
Once the broccoli is cooked as desired, transfer it to an ice bath to stop the cooking. Let rest for a few minutes but do not chill the broccoli for too long. You just want to stop it from cooking.
After the milk mixture has cooked for 2 minutes, remove from heat. Add in the cheddar cheese, ¼ cup at a time, stir until fully melted and incorporated, then repeat. Do until all cheese is mixed in. Do not do this step over any heat as the sauce can break.
Salt the sauce with the pinch of salt if needed.
Pour the sauce over the broccoli and serve. Enjoy!