Heat 2 tsp oil in a large skillet over medium heat. Add onion; cook, stirring often, until soft, 2 to 3 minutes. Add carrots, reduce the heat to low and cook, stirring often, until softened, about 4 minutes. Remove from heat.
Preheat oven to 400 degrees. Transfer the cooked vegetables and rice to a large food processor. Add goat cheese, egg white, basil, jalapeno slices, chile sauce, salt and pepper. Pulse until well blended but still a little coarse. Scrape into a large bowl and stir in toasted almonds. With wet hands, form the mixture into six 3-inch patties (about 1/2 cup each). Heat the remaining 2 tsp oil in a large nonstick skillet over medium heat. Dredge patties in flour and sauté until well browned, 3 to 4 minutes per side. Transfer to a baking sheet and bake until an instant-read thermometer inserted into the middle registers 160 degrees, 8-10 minutes. 6 servings.