Cook broccoli according to package directions (or use fresh if preferred), and set aside.

Dice onion and sauté in butter in the bottom of your soup pot.

Add flour, salt, and pepper, and whisk together.

Add milk and broth, stirring until well blended.

Reduce heat and cook until thickened, stirring often.

Stir in cheese and cooked broccoli.

Warm through and enjoy!