Heat olive oil in a skillet over medium high heat. Add onions and garlic and saute until onions are soft. Remove from heat. Place mushroom mixture in food processor outfitted with steel blade. Add rice and carrots and pulse a few times until mixture has a mealy consistency. Transfer to a large bowl and add bread crumbs and parsley. Mix well and season with salt, pepper and cayenne. Stir in egg. Shape into six patties and broil on a lightly greased baking sheet until browned, about 5 to 7 minutes per side. Nutrition analysis per burger: 234.5 calories, 6 grams protein, 4.6 grams fat, 43 grams carbohydrates, no cholesterol, 229 milligrams sodium, 17.3 percent calories from fat. ----