Marinate the chicken: In a medium bowl, whisk together the beer, ají panca paste, garlic, oil, ají amarillo paste, cumin, and salt. Place the chicken in a large plastic bag, then pour the marinade all over it, turning to coat. Seal the bag tightly, then refrigerate for at least 2 hours, or up to 24 hours.
Make the ají verde: To a blender, add the cilantro, jalapeños, scallions, garlic, queso fresco, ají amarillo paste, lime juice, honey, huacatay, cumin, salt, and ¼ cup cold water. Blend until smooth, then, with the motor running, add the oil in a thin stream until the sauce has thickened. Season to taste with more lime juice and salt, then set aside. (This recipe yields about 2 cups; extra aioli will keep refrigerated in a sealed container for up to 1 week.)
Position an oven rack in the center of the oven and preheat to 450°F. Fit a large rimmed roasting pan with a wire rack.
Remove the chicken from the marinade and transfer it, breast side up, to the prepared roasting pan (discard the marinade). Roast until the chicken is browned all over and its juices run clear when pierced with a fork at the thickest part, 45–55 minutes. Remove the chicken from the oven, transfer to a cutting board, and set aside to rest at room temperature for 10 minutes before cutting into portions. Serve warm, with the reserved aïoli on the side.