Melt butter in a heavy small saucepan over medium heat. Add flour; cook, stirring frequently, until flour mixture is bubbly and golden brown, 1 to 2 minutes. Add milk; bring to a simmer, stirring frequently. Simmer uncovered 1 minute. Remove from heat; stir in cheese until melted.

Cook broccoli with 1 tablespoon water in a covered microwave-safe container on high, 3 to 4 minutes or until crisp-tender, or simmer in water until crisp-tender. Drain; toss with cheese sauce.