Heat your griddle to 375 degrees.
Seed, peel, and slice the avocados into slices each. In a small bowl, toss the avocado slices with the lime juice. Gently toss to evenly coat the slices. Set aside.
In a small bowl, stir the cumin in with the black beans. Set aside.
Place a tortilla on the griddle. Cook for 30 seconds and then flip.
Immediately on one half of the tortilla, add 4 avocado slices, 1/2 cup of cheese, and a few tablespoons of black beans (about 1/4 of the contents of the can).
Fold the empty half of the tortilla onto the toppings. Cook like this for about 2 minutes. The cheese should be starting to melt.
Flip the quesadilla and brown the other side until all the cheese is melted. This should take about 2 minutes. Repeat with remaining tortillas.
Slice into trianglesand serve warm with optional sour cream and salsa and fresh fruit.