Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add cauliflower; cover the saucepan with a lid and steam cauliflower until tender, 10 to 12 minutes.
Melt butter in a large pot over medium heat. Whisk flour into melted butter; cook, stirring constantly until raw flour taste cooks off and mixture darkens, 3 to 4 minutes.
Gradually whisk milk into butter mixture; cook, stirring constantly, until sauce thickens, about 8 minutes. Remove pot from heat; stir in Cheddar cheese. Season sauce with salt and white pepper.
Stir steamed cauliflower into cheese sauce; season with salt and white pepper.