Drain the black beans and rinse them briefly with water. Let them drain while you prepare the rest. Crack six eggs into a large bowl and lightly whisk them. Melt 2 tablespoons of butter in a large skillet over medium-low heat.
Once the butter is melted, pour the eggs into the skillet. Let them cook slowly over medium-low heat. As the bottom layer begins to set, use a spatula to drag the outside edges in towards the center, allowing the uncooked egg to run back into the empty space. Continue to gently move the eggs around in the skillet in this manner until they are about 75% set. The eggs will continue to cook as you add other ingredients, so you do not want to over cook them at this step. Season the eggs with salt and pepper if desired.
Add the drained beans and 2-3 cups of tortilla strips to the skillet. Gently fold them into the eggs, breaking the tortilla strips into smaller pieces as you go. Spoon one cup of salsa over top of the egg mixture and then sprinkle one cup of shredded cheese over top.
Place a lid on the skillet and turn the heat up to medium. Allow the skillet to heat for five minutes, or until mostly heated through. While the skillet is heating, pull the cilantro leaves from the stems and give them a rough chop. Remove the lid and gently fold the ingredients in the skillet, so that the cheese gets a little mixed in and melts slightly. Sprinkle the cilantro over top and serve hot.