Whisk together lime juice, oil, cumin, and cayenne (if desired) in a medium bowl. Add beans; toss well to coat. Season with salt and pepper. Cover, and refrigerate at least 3 hours or overnight.
Toss together mango, cilantro, scallion, and jalapeno in a medium bowl. Refrigerate, covered, until ready to serve.
Preheat oven to 375 degrees. Have a standard muffin tin ready. Sprinkle 1 tablespoon cheese on a nonstick baking sheet to form a rough 3-inch circle. Make 3 more circles. Bake, rotating sheet after 4 minutes, until circles appear lacy and sizzle in middles, 6 to 7 minutes total.
Using a spatula, immediately transfer 1 circle to a cup in muffin tin; gently push down with fingers to form a cup shape. Repeat with remaining circles. Continue forming and baking cheese circles in batches until all cheese is used. Remove cheese cups from tin when cool.
Just before serving, place 1 heaping tablespoon beans and 1 tablespoon mango salsa in each cheddar cup.