In a bowl, coarsely mash beans with a potato masher. Warm a large skillet over medium-high heat; add corn and cook for 3 to 4 minutes, stirring occasionally, until corn begins to brown. Add corn to bowl with beans.
In same skillet, warm oil. Add onion and jalapeño and sauté for 2 minutes. Add garlic and sauté 1 minute longer. Stir mixture into bowl with beans and corn. Let mixture cool to room temperature, about 10 minutes.
When cool, stir in cheese and season with salt and pepper. Preheat oven to 200ºF. Spread a tortilla out on a work surface and spread a 1/2-cup portion of bean mixture over half. Fold tortilla in half. Repeat with remaining tortillas and bean mixture. Warm a large skillet over medium-high heat. Cook as many tortillas as fit in skillet, 3 minutes, then flip quesadillas and cook until golden brown and crispy and cheese is melting, 2 to 3 minutes longer. Place quesadillas on a baking sheet and keep warm in oven while you cook remaining quesadillas. Cut into wedges and serve.
This recipe also appeared in the January 2010 issue.