I start by steaming the broccoli. Cut up about three crowns into bite size pieces and steam until they are bright green. I like a little bite to them but not crunchy. Be careful not to over cook them, you don't want mushy broccoli. You can steam them on the stove or in the microwave. Place the broccoli in a bowl with a 1/4 cup of water and cover with plastic wrap. Poke about 6 holes in the plastic wrap. Microwave for 1 minute at a time, checking to see if it is the desired tenderness.

For the soup, in a saucepan on medium heat, melt butter. Add onions and saute until they are tender, about 2 minutes. Add the salt, pepper, and flour. Stir continually for about 1 minute until smooth and bubbling.

Add the broth and milk. Stir with a whisk, breaking up all the bits of flour/onion mixture. Stir until the mixture boils and thickens. Add the broccoli and turn the heat to low. Simmer, stirring until it is heated through. Add the cheese and stir until melted. (I recommend buying a block of cheese and shredding it yourself. It melts better and tastes better.)