Prepare the brine: In a large soup pot, bring 8 cups water to a boil. Add the kosher salt, peppercorns and garlic; remove from heat. Let cool 30 minutes, then transfer to a large pot or ice chest lined with a large garbage bag. Add another 8 cups water, then add the wings and twist the bag closed. Refrigerate for 4 hours.
Mix all the rub ingredients in a large resealable plastic bag. Drain the wings. Rinse under cool water, pat very dry and put in the bag with the rub. Mix to coat evenly. Seal the bag and refrigerate until ready to cook. (You can do this a day ahead.)
Preheat the broiler. Remove the wings from the bag and place in a single layer on a lightly oiled foil-lined pan. Broil for 8 minutes, then turn and cook for an additional 5 to 8 minutes, or until crisp and golden.
Meanwhile, combine all the ingredients for the salsa, except the olive oil, in a food processor, using salt to taste. Slowly add the oil and puree until smooth. Serve the wings with the salsa.
Photograph by James Baigrie
Recipe courtesy Guy Fieri for Food Network Magazine