Place black beans in a bowl and mash to a smooth consistency.
Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Cook onion in a skillet over medium heat until translucent, about 5 minutes. Add water if needed to prevent sticking. Transfer to the bowl with the black beans.
Stir cooked rice, corn, cornmeal, salsa, garlic powder, cumin, and chili powder into the bean mixture. Mix together, using clean hands, until evenly blended. Roll mixture into 8 equal-sized balls; form balls into patties. Transfer patties to the baking sheet; refrigerate until ready to bake.
Bake burgers on the parchment paper-lined baking sheet for 15 minutes. Flip and bake until heated through and browned, about 15 minutes more.