Chop crown and top tender part of stem into bite size pieces. Set aside.
On high in a medium sized pot boil a quart of water, add the chopped Broccoli and blanch for 2 minutes. Remove from heat drain the hot water and put broccoli in ice bath to stop the cooking process. This will keep the broccoli from getting "soggy" later on.
Put the same pot back on medium heat and melt the butter. Then, add the flour and stir to create a roux. add the beer or broth a tablespoon at a time, constantly stirring, until the roux is dissolved with no lumps. Once you are sure there is no chance of getting flour lumps you can speed up adding the beer. Heat until bubbly then start adding the Velveeta cheese a few cubes at a time, add the remaining ingredients a little at a time constantly stirring until incorporated.
Add the cooked broccoli back in, to heat it back up and serve.
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