In a saucepan, cook broccoli until crisp-tender; drain and set aside. In another saucepan, melt butter; add flour. Cook and stir until thickened and bubbly. Stir in onion. Gradually add milk; bring to a boil and cook for 1 minute. Remove from the heat; stir in cheese, eggs and broccoli. Pour into a greased 2 qt. baking dish. Bake, uncovered, at 325 for 30 minutes.