In a large pot of boiling water, blanch cauliflower until tender, 5 to 7 minutes.
In a large saucepan, melt butter. Sprinkle over flour and cook until slightly golden, 2 to 3 minutes. Pour in milk and whisk until combined. Season with mustard powder, hot sauce, salt, and pepper. Let simmer until it starts to thicken, about 5 minutes.
Turn off heat and stir in cheeses until they are completely melted. Stir in cauliflower and stir until fully coated in cheese sauce.
Season with salt and pepper and garnish with chives. Serve.