1. In a medium pot, combine rice and 3 cups water. Cover pot and bring to a boil. Reduce heat and cook 45 minutes. Remove from heat and let stand 10 minutes.
2. Meanwhile, bring a separate pot of lightly salted water to a boil. Add carrots and cook 2 minutes, until just tender. Drain and toss in 1/2 tsp of the sesame oil.
3. Add 1 tsp of the vegetable oil and remaining 1/2 tsp sesame oil to a large skillet over medium-high heat. Stir in spinach and cook until just wilted, 1 to 2 minutes. Season with salt. Remove to a bowl.
4. Add remaining 2 tsp vegetable oil to skillet. Crack in eggs and fry 2 to 3 minutes each, until whites are set.
5. Divide rice among 4 bowls. Top each with one-fourth of the spinach, carrots and sprouts. Add kimchi, if using. Place 1 egg on top, sprinkle with 1 tsp sesame seeds and dollop with 2 tsp gochujang.