1. In a large skillet over medium heat, heat the 2 teaspoons of olive oil. Add the onion and garlic and cook, stirring until softened, about 5 to 7 minutes. Reduce the heat to low, add the grated carrots, chili powder and cumin and cook for 5 minutes, stirring occasionally. Remove from the heat and let cool.
2. Meanwhile, in a large bowl mash together the black beans, mustard, soy sauce, ketchup and parsley. Stir in the onion and carrot mixture. Add the cooked brown rice and chopped mushrooms, stirring to combine. Season with salt, pepper and cayenne pepper.
3. For the mixture into six patties. Heat the 1 teaspoon of vegetable oil in a nonstick skillet. Add the burgers and cook over medium-low heat, for 5 to 8 minutes per side, until browned and crisp.