In a large, nonreactive container combine the water, orange juice, lemon juice, lime juice, salt, light brown sugar, Southwest Essence, and crushed red pepper and stir until the salt and sugar are completely dissolved.
Add the onions, lime slices, cilantro, garlic, and beer and stir gently to combine.
Add the chicken wings and position so that they are completely submerged in the brine. Cover with plastic wrap and refrigerate for at least 8 hours and up to 12 hours.
Remove the wings from the refrigerator and discard the brining solution. Pat wings dry with paper towels and set aside to come to room temperature for 30 minutes, covered.
Preheat a grill to low.
Brush the wings on both sides with the vegetable oil and sprinkle the Poultry Rub evenly over both sides.
Place wings on grill. Grill the wings, turning occasionally to promote even browning, until they are cooked through and the meat begins to pull away from the bones, 45 minutes to 1 hour.
Serve the wings with both sauces. Let cool briefly before serving.
Combine all of the ingredients in a food processor or blender and process until smooth, about 15 seconds. Scrape down the sides of the bowl with a rubber spatula. Pulse 2 or 3 times. Store in a sterilized container until ready to use.
Preheat oven to 350 degrees F.
Cut the top 1/2-inch off the head of garlic. Put the garlic in an ovenproof dish and drizzle with oil. Cook until garlic is soft, about 1 hour. Set aside until cool enough to handle. Halve the head of garlic widthwise. Press on the garlic to press out the cloves, and then put the garlic in a blender. Add the buttermilk, mayonnaise, Essence, salt, parsley, chives, and zest and pulse until blended. Cover and refrigerate until ready to use.
Combine all ingredients thoroughly.
Recipe from "New New Orleans Cooking", by Emeril Lagasse and Jessie Tirsch, published by William Morrow, 1993.
Recipe from Emeril Lagasse