Place the beans in a medium bowl and mash with a fork until chunky. Add 1 cup of the sprouted quinoa, flour, garlic, onion, and chili powder; stir to combine. Season with salt to taste, then fold in the egg.
Heat the oil in a large skillet (preferably cast iron) over medium heat.
Divide the mixture into four balls and use your hands to shape each into patties. Carefully place the patties in the hot skillet and cook until browned and crispy, about 4 minutes, before flipping and cooking for an additional 3-4 minutes until golden brown and crispy on both sides.
Toast burger buns, if you like. Smear avocado onto the inside bottoms of the buns and set the patties on top. Spoon the salsa over the patties, add the top half of the bun, and serve.
I used oat flour in order to keep the patties gluten-free, but you can also use all-purpose wheat flour or gluten-free all-purpose flour. If you eat a gluten-free diet, substitute gluten-free buns for regular buns. You can also go bun-less by wrapping the patty with lettuce, which is how I often eat my burgers.