In a skillet, combine black beans and liquid with the garlic, chipotle powder, sea salt and lime juice. Heat over medium-low and cook until the majority of liquid has been absorbed, 6 to 8 minutes.
Meanwhile, scoop the avocado from its shell and place it in a bowl. Add the minced cilantro and lime juice; mash with a fork until avocado is in small chunks.
Preheat a griddle or large, flat skillet over low heat. Brush one side of a tortilla with olive oil and place it oil-side down on a plate or other clean surface. Sprinkle with 1/4 of the cheese, followed by 1/2 the black beans, 1/2 the avocado mixture, and finish with another layer of cheese. Place another tortilla on top and brush the top side with olive oil. Repeat with remaining ingredients to make a second quesadilla.
Cook the quesadilla over low heat, flipping once, about 4 to 5 minutes. The tortilla should be browning and crisp and the cheese should be melting. Repeat with second quesadilla. Cut into wedges to serve.