In a large bowl, whisk together olive oil, lime juice, garlic, cumin, smoked paprika, oregano, salt, and pepper. Add the chicken pieces and toss to coat thoroughly. Cover the bowl and marinate for at least 4 hours or overnight.
Preheat your oven to 425°F (220°C). Line a baking sheet with foil and place a wire rack on top. Arrange the marinated chicken on the rack, skin side up.
Bake for 40 to 45 minutes until chicken reaches an internal temperature of 165°F (74°C) and the skin is golden. Optionally broil for the last 3 minutes for extra crispiness.
While the chicken roasts, prepare the creamy green sauce by blending mayonnaise, sour cream, cilantro, parsley, jalapeños, garlic, lime juice, olive oil, and salt until smooth.
Remove the chicken from the oven, let it rest, then serve hot with the creamy green sauce on the side.
Notes
For a spicier sauce, keep some seeds in the jalapeños. You can also substitute sour cream with Greek yogurt for a lighter option.