Arrange broccoli in a steamer. Steam, covered, 4 minutes or until crisp-tender. Place broccoli in a large bowl.
Whisk 1/4 cup beer and flour in a bowl. Combine milk and 1/4 cup beer in a pan; bring to a simmer. Stir in flour mixture; bring to a boil. Reduce heat; simmer 2 minutes. Add cheddar, chives, lemon rind, and kosher salt. Pour over broccoli.