In the bowl of a food processor, puree the black beans until most of the beans are chopped. You don't want it to be hummus texture - you want it to have lumps. Then add 2 tablespoons of olive oil, green onions, cilantro, garlic, Parmesan cheese, and bread crumbs. Pulse until ingredients are well combined.
Pour out the mixture onto a piece of parchment paper. Separate the mixture into 6 even portions. To do this, cut in half, then cut the halves in thirds. Form each portion of black bean mixture into a burger shape.
Heat the remaining olive oil over medium high heat in a skillet. Fry the black bean cakes on each side for 5-6 minutes, or until the black bean cakes are crispy on the outside. Cook no more than 2 at a time. Place on a plate, lined with a paper towel, after cooking.
To Assemble Sandwich
Place a cooked black bean cake on top of a piece of toast. Lay a fried egg, yolk up, on top of the black bean cake. Put a dash of salsa and sour cream on egg, then sprinkle green onion and cilantro on top. Add salt and pepper to taste.