Step 1

Preheat grill to medium-high. Stir mayonnaise, sour cream and barbecue sauce together in a small bowl until combined. Set aside.

Step 2

Slice pointy stem end off of onion; remove and discard peel, keeping root end intact. Place the onion, cut-side down, on a cutting board. Leaving a 1/2-inch rim around the root, make 4 evenly spaced lengthwise cuts from the root end down to the stem end. (This will create 4 onion sections.) Repeat the process to make 3 additional lengthwise cuts in each onion section, creating 16 sections total. Turn the onion over. Using your hands, separate layers of 16 "petals" as needed, keeping the onion intact at the root end.

Step 3

Place the onion on a sheet of foil. Stir Parmesan, paprika and Italian seasoning together in a small bowl. Sprinkle the mixture between the petals of the onion; drizzle with oil.

Step 4

Place the foil sheet with the onion on the grill rack; grill, covered, until tender and lightly charred, 20 to 24 minutes. Serve with the mayonnaise sauce.