Step 1Heat the oven to 300 degrees. Toast the pine nuts until very lightly browned, 8 to 10 minutes. Cool.
Step 2Place the turkey cutlets in a shallow dish. Add the olive oil and salt and pepper to taste and turn to coat all sides. Set aside while heating a grill.
Step 3Combine the piquillos, pine nuts, pine nut oil and peanut oil in a blender and process until smooth. Season with salt to taste. Add a splash of vinegar if desired.
Step 4Grill the turkey until just done, about 2 to 3 minutes on each side. Divide among serving plates and spoon piquillo sauce in a ribbon over the cutlets, passing the remainder on the side. (Makes two-thirds cup sauce.)