In a small bowl, whisk together the olive oil, lime juice, cumin, salt, pepper, 4 cloves minced garlic, soy sauce, aji amarillo paste, and honey until combined.
Place chicken in a bowl or baking dish and pat completely dry with a paper towel. Coat completely in the marinade, then let rest for 30 minutes at room temperature or overnight in the refrigerator.
When ready to roast, preheat the oven to 350F. Place the chicken in a roasting dish or cast iron skillet and brush with the remaining marinade from the bottom of the marinade bowl.
Roast the chicken for 1 hour, 30 minutes, basting every 30 minutes, until internal temperature registers between 155 to 160 F. If your chicken is less than 4 pounds, begin checking the temperature at 1 hour. If the chicken is close to 5 pounds, adjust time accordingly until internal temperature is reached.
While the chicken is roasting, prepare the aji verde sauce. Combine yogurt, jalapeño, aji amarillo pepper, lemon juice, cotija cheese, 2 cloves garlic, apple cider vinegar, and a pinch of salt in a blender. Blend until completely smooth. Taste; season with more salt if needed. If the sauce is too spicy, add a dollop more of yogurt.
Once the chicken is roasted and reads 160 F, remove it from the oven and tent it with foil for 5-10 minutes, until the temperature reaches 165 F.
To serve, carve the chicken into pieces and serve with aji verde sauce.