For the Sauce: Combine jalapeños, ají amarillo (if using), cilantro, garlic, mayonnaise, sour cream, lime juice, and vinegar in the jar of a blender. Blend on high speed, scraping down sides as necessary, until smooth. With blender running, slowly drizzle in olive oil. Season to taste with salt and pepper. Sauce will be quite loose at this point, but will thicken as it sits. Transfer to a sealed container and refrigerate until ready to use.

For the Chicken: Pat chicken dry with paper towels and place on a large cutting board, breast side down. Using sharp kitchen shears, remove backbone by cutting along either side of it. Turn chicken over and lay out flat. Press firmly on breast to flatten chicken. For added stability, run a metal or wooden skewer horizontally through chicken, entering through one thigh, going through both breast halves, and exiting through other thigh. Tuck wing tips behind back.

Combine salt, cumin, paprika, pepper, garlic, vinegar, and oil in a small bowl and massage with fingertips until homogeneous. Spread mixture evenly over all surfaces of chicken.

to ROAST: Adjust the oven rack to the lower-middle position, and preheat the oven to 425 degrees. Line a roasting pan with aluminum foil for easy clean-up. Spray a rack (preferably a v-shape) with non-stick cooking spray and place the chicken on top. Tie the legs together with kitchen string. Roast for 20 minutes, until the skin is golden. Turn the heat down to 375 degrees, and continue to roast for about an hour and ten minutes more, or until the juices run clear when you cut between the leg and thigh. (Keep an eye on it -- if it's browning too quickly, cover it loosely with foil.) Tent the chicken with foil and let rest for about 20 minutes. Tilt the chicken over the roasting pan to release the juices, then transfer to a cutting board. Carve the chicken and serve with green sauce.

TO GRILL: Light a chimney full of charcoal. When all charcoal is lit and covered with gray ash, pour out and spread coals evenly over half of coal grate. Alternatively, set half the burners of a gas grill to high heat. Set cooking grate in place, cover grill, and allow to preheat for 5 minutes. Clean and oil grilling grate. Place chicken, skin side up, on cooler side of grill, with legs facing toward hotter side. Cover grill, with vents on lid open and aligned over chicken. Open bottom vents of grill. Cook until an instant-read thermometer inserted into thickest part of breast registers 110°F (43°C). Carefully flip chicken and place, skin side down, on hotter side of grill, with breasts pointed toward cooler side. Press down firmly with a wide, stiff spatula to ensure good contact between bird and grill grates. Cover and cook until skin is crisp and an instant-read thermometer inserted into thickest part of breast registers 145 to 150°F (63 to 66°C), about 10 minutes longer. If chicken threatens to burn before temperature is achieved, carefully slide to cooler side of grill, cover, and continue to cook until done. Do not leave the lid off for longer than it takes to check temperature, or chicken will burn.

Transfer chicken to a cutting board and allow to rest for 5 to 10 minutes. Carve and serve with sauce.