Bring a small saucepan of salted water to a boil. Add the edamame and cook until tender, about 5 minutes; drain. In a large saucepan, melt the butter in the olive oil. Add the shallots and garlic and cook over moderate heat until softened, about 3 minutes. Add the rice and cook, stirring, until slightly translucent, about 2 minutes.
Mix the chicken broth with the beer and season generously with salt and pepper. Add 1 cup of the beer broth to the rice and cook over moderately high heat, stirring constantly, until nearly absorbed. Continue adding the broth, about 1 cup at a time, stirring until it is absorbed before adding more. The rice is done when it's al dente and suspended in a thick, creamy liquid, about 17 minutes total. Add the edamame and cheese and stir until the cheese is melted. Season with salt and pepper and serve right away.