For the brine: Stir the kosher salt, brown sugar into 1-quart cool water until dissolved.
Mix ¼ cup olive oil, 2 teaspoons minced garlic, flat leaf parsley, red pepper flakes, and dry white wine in a small bowl and set aside.
Remove the shrimp from the brine. Wash and dry throughly. Toss them with the marinade, coat and marinate for 1-hour, covered in the refrigerator.For the salsa: In a food processor, combine the tomatillos, remaining teaspoon garlic, and serrano chile; pulse to finely chop.
Add the avocado and green onion and pulse til just blended. The finished salsa should have some texture.
Place the salsa in a small bowl and toss with the extra-virgin olive oil, lemon juice, salt and pepper. Store, covered and refrigerated up to 2 hours. Toss with cilantro just before serving.To grill the shrimp: Light a charcoal fire.
Drain the shrimp from the marinade.
Place the 6 shrimp on a work surface in front of you alternating the shrimp left and right, tucking them into themselves, following their natural shape. Secure the shrimp with 2 skewers so that they grill evenly and turn over easily.Grill the shrimp over medium-hot coals until they are barely cooked through, about 3 to 4 minutes total, turning halfway through. Grill the lemon slices until softened and well marked by the grill.
Place the shrimp and lemon slices on plates and top with the salsa.