In a pot over medium heat melt the butter.
Sprinkle with flour and cornstarch, whisk until thickened. Cook, whisking continually for three minutes. Slowly whisk in the milk and the beer, stirring to make sure no lumps remain.
About ¼ cup at a time, add the cheese, whisking between addition until the cheese has completely melted. Make sure to adjust heat to make sure it does not boil.
Preheat oven to 400.
Add the broccoli to a baking sheet. Drizzle with olive oil, sprinkle with garlic and salt. Toss to coat.
Roast at 400 for 10-15 minutes until fork tender and edges have started to crisp.
Serve with cheese sauce on the side or drizzled on top.