Pound the chicken breasts until they are even thickness. (If your chicken breasts are quite large, pound them to an even thickness and then cut them in half so that each piece equals about 7-8 oz each). Pat the chicken dry with paper towels. Sprinkle the salt and pepper over the chicken breasts.
In a shallow dish (I use a pie tin) add the flour, cayenne pepper and cardamom. Mix to incorporate the ingredients. Dredge the chicken breasts in the flour. Place the flour coated chicken breasts on a plate while you prepare the skillet.
Heat a 12 inch cast iron skillet over medium heat. Once the skillet is hot, add 2 tablespoons of the vegetable oil and heat until just smoking. Place the chicken in the skillet, and brown each chicken breast for about 4 minutes on each side. Once done, transfer the chicken breasts to a plate to rest.
Add 1 tablespoon of vegetable oil to the empty skillet (still over medium heat). Add the carrots and onions to the skillet. Cook until softened, about 5 minutes.
Stir in the garlic, rice, and curry powder. Mix to combine. Add the chicken broth. Bring the mixture to a gentle simmer. Add the chicken into the skillet. Cover. And cook for 8-10 minutes or until the chicken reaches an internal temperature of 160°F.
When chicken reaches 160°F, remove the chicken from the skillet and place it on a plate. Tent the plate with aluminum foil, and let it sit for 10 minutes.
Add the coconut milk to the rice. Stir to combine. Cover the skillet and cook for 10-12 minutes or until the rice has absorbed all of the liquid.
Add the peas to the rice, stir to combine.
Remove from heat and gently stir the cilantro into the rice. Serve immediately with the chicken.