Roughly mash black beans, quinoa, chopped chipotle peppers, tomato paste, cilantro and bread crumbs until thoroughly combined and sticky. If you are using canned black beans instead of homemade, add 1 tsp each of cumin and salt.
Cover and refrigerate for 30 minutes.
Heat a cast iron skillet over medium heat. Divide the cooled quinoa and black bean mixture into four equal parts, and form into patties. To ensure your burgers stay together, start by rolling the mixture into a ball, then gently flatten them out into a patty about the same circumference as your buns.
Once pan is hot, scoot patties into the pan and allow to cook for 10 minutes without touching them. Gently flip and cook for 7 minutes on the other side.
Brush the inside of buns with olive oil, and broil inside facing up in the oven for 2-3 minutes until crisp and brown.
Place a cooked burger atop each bun. Top each with a slice of cheese, and return to oven to broil for 1-2 minutes until cheese is bubbling.
Assemble the rest of the burgers with avocado and spring mix. Slice in half and serve with a side chipotle of chipotle ketchup.