Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.
Combine rice, beans, sweet potatoes, roasted red bell peppers, tomatoes, green onions, carrots, cilantro, chili powder, garlic, hot pepper sauce, and cumin in a large bowl; mix well. Form mixture into 4 equal patties; place on the prepared baking sheet.
Bake in the preheated oven for 15 minutes. Flip patties; bake until browned and slightly crisp, about 15 minutes more.
To freeze these burgers, bake and cool, then wrap in aluminum foil or freezer-safe wrap. To reheat, unwrap the burgers and reheat them in the microwave, or place them on a parchment-lined pan and bake in a 300-degree oven until hot, about 25 minutes.