Puree the cilantro stems, lime zest, juice, Worcestershire, chile, garlic, 3/4 tsp. of the salt, and the pepper in a blender until smooth. With the motor running, add the butter, blending until it is incorporated. Transfer the sauce to a large bowl.
Pat the wings dry, then halve them at the joint and season them with the remaining 1 tsp. salt.
Heat 1 inch of oil in a pot or deep heavy skillet to 400°F. Fry the wings in 2 or 3 batches, turning occasionally, until they are golden and cooked through, about 8 minutes per batch (return the oil to 400°F between batches). As they are cooked, transfer the wings to the bowl with the sauce, tossing them to coat, or serve the sauce on the side for dipping. With tongs or a slotted spoon, transfer the wings to a serving plate and sprinkle with the cilantro leaves. Serve the wings with the remaining sauce on the side.