01 - In a large bowl, whisk together the olive oil, soy sauce, lime juice, minced garlic, cumin, smoked paprika, oregano, black pepper, salt, and chili powder until a smooth, fragrant paste forms.
02 - Pat the butterflied chicken thoroughly dry with paper towels. Rub the marinade generously over and under the skin, ensuring even coverage. Cover tightly and refrigerate for at least 2 hours, or ideally overnight for maximum flavor penetration.
03 - Preheat the oven to 425°F. Line a roasting pan with aluminum foil and set a wire rack on top. Place the chicken skin-side up on the rack.
04 - Roast the chicken for 45 to 55 minutes, until the skin is deeply golden and crisp. Verify doneness by inserting a kitchen thermometer into the thickest part of the thigh — it should register 165°F. Allow the chicken to rest for 10 minutes before carving.
05 - While the chicken rests, combine the cilantro, jalapeño or serrano chile, garlic, mayonnaise, sour cream, lime juice, Parmesan cheese, and olive oil in a blender or food processor. Blend until completely smooth and creamy. Season with salt and pepper to taste.
06 - Carve the rested chicken into serving pieces and arrange on a platter. Drizzle generously with the green sauce, passing additional sauce at the table.