Lay the onion on its side. At the pointed end (not the root), slice about one-half inch off of the onion. Remove the skin.
Lay the onion cut-side-down, root side up.
Place your knife point about ¼-inch from the root and slice down. Rotate the onion and continue making slices every ¼ to ½ inch.
Turn the onion over and gently separate the petals.
In a deep bowl large enough to fit the onion, combine the BBQ sauce and beaten egg. Dip the onion into the sauce, working the sauce onto every petal.
In another bowl, combine the breadcrumbs, salt, garlic powder and Cajun seasoning. Sprinkle the breadcrumbs onto every petal. Repeat with the second onion.
Heat the grill to 400 degrees. Place the skillets on the grill and cook with the lid closed for 30 minutes.
Mix the mayonnaise with 2 tablespoons of BBQ sauce. Serve as a dipping sauce.