In a small bowl, whisk together soy sauce, 2 tablespoons lime juice, 4 cloves minced garlic, cumin, paprika, oregano, black pepper, and oil to create the marinade.
Place the chicken in a large resealable bag or baking dish and coat thoroughly with the marinade. Refrigerate for at least 4 hours.
Preheat oven to 425°F (220°C).
Place the chicken on a wire rack set over a rimmed baking sheet and roast for 50 to 60 minutes until the internal temperature reaches 165°F (74°C).
While the chicken roasts, prepare the Aji Verde sauce by blending jalapeños, cilantro, 2 garlic cloves, mayonnaise, sour cream, 1 tablespoon lime juice, and salt in a food processor until smooth.
Allow the chicken to rest for 10 minutes before carving.
Serve the chicken accompanied by the green sauce.