Heat sesame oil in large nonstick skillet over high heat. Add carrot and next 3 ingredients, and stir-fry until tender. Add cooked rice; stir-fry 2 minutes. Push rice mixture to sides of pan, forming a well in center. Add egg to center of pan, and let cook 30 seconds; toss with rice, and stir-fry until egg is cooked. Stir in soy sauce and water; cook until thoroughly heated.
Use instant brown rice to save time—it's ready in 10 minutes.