Remove the chicken from the refrigerator and pat dry with paper towels. Season generously with salt and black pepper.
Add the olive oil to a large (12-inch) skillet set over medium-high heat. Add the chicken, skin-side-down, and cook for approximately 6-8 minutes on each side, or until golden brown. Avoid over-crowding the pan and cook in batches if necessary. Transfer chicken to a clean plate and set aside.
Return the pan to medium heat. Sauté the diced onions, red bell pepper, and carrot in the reserved fat from the chicken skin (and/or add an additional tablespoon of olive oil, if needed) until softened, about 8-10 minutes.
Once the vegetables have softened, stir in the minced garlic, ground coriander, ground cumin, tomato paste, and fresh mint. Mix well to combine and cook for an additional 1-2 minutes.
Add the rice and frozen peas and mix to combine with the veggies and tomato paste. Toast the rice for a minute or so, stirring continuously.
Add the chicken broth (or chicken stock) to the rice. Mix well to combine and bring to a high simmer. Carefully distribute the browned chicken pieces over the rice mixture and cover with a tight-fitting lid. Reduce heat to low, and cook for approximately 25 minutes, or until the chicken is fully cooked and the rice has absorbed all of the liquid.
Remove from heat and allow the chicken and rice to rest, covered, for 5-10 minutes before serving. Served garnished with fresh mint and lemon juice, if desired.