Step 1: Prepare the Chicken Marinade. In a medium bowl, combine the aji amarillo paste, minced garlic, 1 tablespoon lime juice, ground cumin, paprika, dried oregano, 1/4 teaspoon salt, 1/8 teaspoon black pepper, and 1 tablespoon olive oil. Mix well.
Step 2: Marinate the Chicken. Add the chicken thighs to the bowl with the marinade, ensuring each piece is thoroughly coated. Cover the bowl and refrigerate for at least 30 minutes, or up to 4 hours for deeper flavor.
Step 3: Make the Aji Verde Sauce. While the chicken is marinating, prepare the green sauce. In a blender or food processor, combine the packed cilantro, mayonnaise, Greek yogurt, jalapeños (start with one and add more to taste, adjusting for heat by removing seeds), 1 clove garlic, 1 tablespoon lime juice, 1/4 teaspoon salt, and 1/8 teaspoon black pepper. Blend until completely smooth and creamy. If the sauce is too thick, add a teaspoon of water or olive oil at a time until desired consistency is reached. Taste and adjust seasoning if needed.
Step 4: Cook the Chicken. Preheat your grill or a grill pan to medium-high heat. If using an oven, preheat to 400°F (200°C). Place the marinated chicken on the hot grill and cook for 6-8 minutes per side, or until the internal temperature reaches 165°F (74°C). If baking, arrange chicken on a baking sheet and bake for 20-25 minutes, or until cooked through.
Step 5: Rest and Serve. Once cooked, remove the chicken from the heat and let it rest for 5-10 minutes before slicing. This helps retain the juices. Serve the sliced Peruvian chicken generously topped with the vibrant Aji Verde green sauce.