1Cook broccoli according to package directions, except be careful not to over cook. Drain well. Set aside.
2Melt butter in a large saucepan and saute onion in this butter. Cook until onion is translucent. Keep heat on medium and add flour, stirring to mix as you add. Then slowly pour in half and half, broth, and add salt and pepper.
Continue to cook with heat on medium. Stir constantly until mixture begins to thicken. Do NOT let mixture come to a boil.
3Add chese and continue to stir and cook until cheese is melted. Remove from heat and stir in broccoli. Serve immediately. Garnish with a bit of reserved broccoli or a little grated cheese, if desired.