Preheat the oven to 350°F. Grease a large nonstick skillet or 9"x13" baking dish. Bring a large pot of generously salted boiling water (it should taste like the sea) to a boil. Cook the orzo until al dente according to package directions; drain well and toss with the oil to prevent sticking. 

In the same pot you used to cook the pasta, heat the butter over medium heat until foamy, and then add the garlic. Cook, stirring, until fragrant. Add flour and cook, stirring, until a light golden paste is formed, 2 minutes. Add the milk and beer, raise the heat to medium-high, bring to a boil, then reduce heat to medium and cook until the mixture is thickened, 3–4 minutes. Stir in 3 cups of the cheese, salt, and cayenne until the cheese is melted, then stir in the orzo and broccoli. Season with more salt to taste, then pour into the prepared baking dish or skillet, top with the remaining ½ cup cheese, and bake until the top is golden and bubbly, 40 minutes.