In a large skillet set over low heat, heat 1 tablespoon peanut oil. Stir in the onion and red pepper, cooking until tender, 5 to 6 minutes. Add diced carrots and continue to cook for another 5 to 6 minutes, until carrots are slightly soft. Stir in brown rice, soy sauce, rice vinegar, and mirin, cooking for 2 to 3 more minutes to fry the rice.
Create a large well in the center of the rice and add remaining tablespoon of peanut oil. Whisk the eggs in a bowl, then pour them into the well. Cook the eggs, stirring occasionally, until set, 3 to 4 minutes. Stir in sesame seeds, then serve hot with a sprinkle of cilantro.