Chop broccoli into florets. Steam for 10-15 minutes until stems are fork-able but still firm.
Melt butter in sauce pan over low heat. Whisk in flour. Slowly pour in milk and beer, whisking constantly until no lumps remain, about 2-3 minutes. Add cheese a little at a time, whisking constantly, and making sure cheese is completely melted before adding more cheese. Continue until all cheese has been incorporated. Once all cheese has been added, whisk until cheese sauce is thick and smooth, about 3-5 minutes.