In a small bowl combine cream cheese and Monterey jack cheese. Set aside.
Place in a food processor 2 cups black beans, egg, onion, garlic, jalapeno, sweet peppers, pepper, salt, soy sauce and cilantro, processed at medium speed until all ingredients are well combined.
Transfer the mixture to a medium bowl and add the remaining cup of black beans and bread crumbs. Mix using a wooden spoon.
Divide and form the mixture into 12 equal patties. Place 1 tablespoon of the cream cheese mixture onto 6 of the patties, and then top with the remaining 6 plain patties. Completely pinch sides closed to seal in the mixture and reform patties.
Heat grill to medium-high heat. Spray or brush the grill first with a little bit of oil will prevent burgers from sticking.
Cook the patties for about 3 - 5 minutes per side. You'll know you are ready when the surface of this lightly browned. These patties are mighty fragile so be careful when turning. After cooked the patties will set up nicely for you.
Assemble burgers on buns with greens, tomato, and avocado. Top it with chipotle mayo. Enjoy!