Drain and rinse black beans, chop cilantro, juice the lime, and mix cilantro, lime juice, and sour cream in a small bowl; set aside.
Warm a large skillet or griddle over medium-high heat, brush one side of a tortilla with butter, place buttered-side down, sprinkle cheese and beans on one half, fold in half, and cook 2 minutes per side until golden and cheese melts; repeat with remaining tortillas.
Cut quesadillas into triangles, divide among four plates, and serve with cilantro lime sour cream for dipping.
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