In a small saucepan, heat the olive oil over medium-high heat. Add the garlic and cook until golden, about 1 minute. Stir in the black beans and jalapeños and cook, lightly mashing the mixture against the side of the pan, for 2 minutes.
Stir the beer into the black bean mixture and bring to a boil. Cook, continuing to mash, until thickened, about 10 minutes. Stir in the corn and tomatoes and cook, stirring, until heated through, about 5 minutes. Stir in the lime juice; set aside.
Lay the tortillas on a work surface. Sprinkle the cheese in the center and spoon about 1/4 cup bean mixture on top. Fold the tortilla burrito-style.
Heat a large skillet over medium-high heat. Place the burritos folded side down in the skillet and cook until browned, about 1 minute on each side.