Step 1: Make the Creamy Green SauceCombine the jalapeños, ají amarillo paste, cilantro, garlic, mayonnaise, sour cream, lime juice, and vinegar in your blender. Blend on high speed until completely smooth. With the blender running on low, slowly drizzle in the olive oil to emulsify. Season generously with salt and pepper. Transfer to an airtight container and refrigerate for at least 30 minutes to thicken.
Step 2: Prepare the ChickenSpatchcock the chicken: place it breast-side down and use kitchen shears to cut out the backbone. Flip the chicken over and press firmly on the breastbone to flatten it. Pat the entire chicken completely dry with paper towels.
Step 3: Marinate the ChickenIn a small bowl, mix salt, cumin, paprika, pepper, minced garlic, vinegar, and oil into a paste. Rub about a third of the marinade under the skin of the breasts and thighs. Rub the remaining marinade all over the outside.
Step 4: Grill the Chicken to PerfectionSet up a two-zone grill (one hot side, one cool side). Place the chicken skin-side up on the cooler side and cook, covered, until an instant-read thermometer in the breast registers 110°F (43°C).
Step 5: Crisp the SkinMove the chicken skin-side down to the hotter side of the grill. Cover and cook until the skin is deep golden brown and crisp, and the breast temperature reaches 145-150°F (63-66°C). Watch closely to prevent burning.
Step 6: Rest and ServeTransfer the chicken to a cutting board and let it rest for 10 minutes. Carve and serve immediately with the chilled creamy green sauce.