Rinse the rice under cold water until the water runs clear. Place it in a medium saucepan with 3 cups of water and a pinch of salt. Bring to a boil, then reduce the heat to low, cover, and simmer for 15 minutes until the water is absorbed. Remove from heat and let it sit covered while you cook the chicken.
In a small bowl, stir together the gochujang, soy sauce, honey, and minced garlic until smooth.
Heat the sesame oil in a large skillet over medium-high heat. Add the chicken pieces and cook for 5 to 6 minutes, stirring occasionally, until they start to brown.
Add the sliced carrots to the skillet and cook for another 3 minutes. Pour the gochujang sauce over the chicken and carrots. Stir well to coat everything. Reduce the heat to medium and cook for 6 to 8 minutes until the chicken is cooked through and the carrots are tender but still have some bite.
Fluff the rice with a fork and divide it among four bowls. Spoon the chicken and carrots over the rice. Sprinkle with sliced green onions and sesame seeds before serving.