In a mixing bowl, whisk together the soy sauce, lime juice, minced garlic, olive oil, aji amarillo paste, smoked paprika, cumin, oregano, black pepper, and honey to create the marinade.
Pat the whole chicken completely dry with paper towels. Rub the marinade all over the chicken, carefully working it under the skin of the breast and thighs, as well as inside the cavity.
Place the marinated chicken in a large dish, cover tightly, and refrigerate for at least 6 hours, preferably overnight.
Preheat your oven to 400°F (200°C). Arrange the potato wedges around the edges of a large roasting pan and place the marinated chicken in the center.
Roast the chicken for 60 to 75 minutes, basting occasionally with pan juices, until the skin is deeply golden and crispy, and a meat thermometer inserted into the thickest part of the thigh reads 165°F (74°C).
While the chicken is roasting, prepare the Aji Verde sauce. In a blender or food processor, combine the cilantro, jalapenos, cotija cheese, mayonnaise, and a pinch of salt. Blend until smooth and creamy. Refrigerate until ready to serve.
Remove the chicken from the oven and loosely tent with foil. Allow it to rest for 15 minutes before carving to keep the juices inside.
Carve the chicken into quarters or pieces and serve warm alongside the roasted potato wedges and a generous drizzle of the Aji Verde sauce.