Season chicken pieces with 1 teaspoon salt and black pepper on all sides.
Heat olive oil in a large, deep skillet or Dutch oven over medium-high heat, then brown the chicken pieces on all sides, about 4-5 minutes per side. Remove chicken and set aside.
In the same skillet, add onion and bell pepper, cooking for 5 minutes until softened, then add garlic and cook for 1 minute more.
Stir in the rice, diced tomatoes with their juices, chicken broth, saffron, cumin, paprika, and remaining 1 teaspoon salt, mixing well to combine.
Nestle the browned chicken pieces into the rice mixture, bring to a boil, then reduce heat to low, cover, and simmer for 25-30 minutes until rice is tender and chicken is cooked through.
Stir in frozen peas, cover, and let sit for 5 minutes, then garnish with fresh cilantro before serving.