Steam broccoli, covered, in a steamer basket over boiling water 5 minutes or until crisp-tender. Keep warm.
Melt butter in a heavy saucepan; add onion, and sauté until tender. Add flour and bouillon granules, stirring until blended. Cook, stirring constantly, 1 minute. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in 1/2 cup cheese and next 4 ingredients; pour over broccoli. Sprinkle with additional cheese, if desired.
I forgot to purchase marjoram, so i used oregano instead, but this still turns out delicious! I served this with chicken and pasta. Constantly stirring can be a pain, but is well worth it for this flavorful cheese sauce.