Sear the Chicken: In a large heavy-bottomed pot or Dutch oven, heat 2 tablespoons of oil over medium-high heat. Season the chicken pieces generously with salt and pepper. Sear the chicken until golden brown on all sides (approximately 5 minutes per side). Remove the chicken from the pot and set aside.
Prepare and Sauté the Base: Add the remaining tablespoon of oil to the same pot. Sauté the diced red onion until translucent, about 5 minutes. Stir in the minced garlic and Aji Amarillo paste, cooking for another 2 minutes. Meanwhile, blend the cilantro leaves with 1/2 cup of chicken stock until completely smooth. Pour this cilantro mixture into the pot and sauté for 3-5 minutes until the paste thickens and turns a deeper green.
Simmer the Broth and Rice: Return the seared chicken pieces to the pot. Add the remaining chicken stock and the rinsed rice. Bring the mixture to a boil, then reduce the heat to low. Cover the pot and simmer for 15 minutes.
Integrate Hearty Vegetables: Add the diced potatoes, carrots, corn, and julienned red bell pepper to the pot. Re-cover and continue to simmer for an additional 20-25 minutes, or until the chicken is fully cooked, the rice is tender, and the potatoes are soft.
Finish and Garnish: Stir in the frozen peas and lime juice. Cook for 2-3 more minutes until the peas are bright green and tender. Taste and adjust seasoning with additional salt and pepper as needed. Serve hot in large bowls, ensuring each serving contains chicken, rice, and a variety of vegetables.