Whisk the egg whites in a bowl with the cumin, chili powder, and 1/4 tsp salt until slightly frothy. Set aside.
Heat 1 tsp of the olive oil in a 10-inch nonstick skillet over medium heat. Add the bell pepper, onion, and jalapeno, and cook for 3 to 4 minutes, stirring, until softened.
Push the vegetables to one side of the skillet, pour in the egg whites, and scramble for 2 to 3 minutes until they're opaque and no longer glossy. Transfer everything to a plate.
Wipe out the skillet. Add the black beans and 2 tbsp water, and cook over medium heat for 2 minutes, stirring, until warmed through. Lightly mash a few beans with the back of a spoon.
Lay one tortilla flat on a work surface. Scatter 2 tbsp of the cheese over it, then top with half the egg mixture and half the bean mixture, followed by another 2 tbsp cheese. Top with a second tortilla and press gently.
Heat the remaining olive oil in the skillet over medium heat. Slide the quesadilla in and cook for 3 to 4 minutes per side, pressing down with a spatula, until golden brown and the cheese has melted.
Transfer to a cutting board and repeat with the remaining tortillas and filling to make the second quesadilla.
Cut each quesadilla into wedges and top with cilantro. Serve hot with salsa, avocado, and lime wedges.