Place broccoli in a steamer over 1 inch of boiling water, and cover. Cook until tender but still firm, about 2 to 6 minutes. Drain and transfer to a serving dish.
Melt butter in a saucepan over medium heat; whisk in flour until smooth. Slowly stir in milk. Cook and stir until mixture thickens, about 3 minutes.
Add freshly grated cheddar cheese and stir until cheese is melted, about 3 minutes more. It's important to use freshly grated since packaged shredded cheese is coated with flour, which can prevent the sauce from coming together.
Pour the cheese sauce over the steamed broccoli and season with salt and pepper.
