Heat the vegetable oil in a large skillet over medium heat. Add the chicken pieces and season with salt and black pepper. Cook for 5 to 6 minutes, stirring occasionally, until the chicken is lightly browned on all sides.
Add the diced onion and minced garlic to the skillet. Cook for 2 minutes until the onion softens.
Stir in the red curry paste and cook for 1 minute to release its aroma.
Pour in the coconut milk and chicken broth. Add the rinsed jasmine rice, sliced carrots, and chopped red bell pepper. Stir everything together and bring the mixture to a gentle boil.
Reduce the heat to low, cover the skillet, and simmer for 18 minutes without lifting the lid.
Remove the lid and stir in the frozen peas. Cover again and cook for 3 more minutes until the peas are heated through and the rice is tender.
Turn off the heat and let the dish rest covered for 5 minutes. Fluff with a fork and sprinkle with chopped cilantro before serving if desired.