Prepare grill or heat grill pan on stove top. Soak wooden skewers in water for 30 minutes.
Lay an onion slice on a flat work surface. Poke the skewer through center of the 1/2-inch-thick side of the onion slice, carefully pushing the skewer all the way through the onion slice and out the other side. The skewer and onion should resemble something like a lollipop. If the skewer is long enough push another onion slice onto the skewer. Skewer the remaining onion slices in the same manner. Brush onions on both sides with thin coats of oil and season generously with salt and pepper. Grill the onions, flipping occasionally, until browned and lightly charred, about 10 to 15 minutes. Remove to a platter and allow to cool.
In a large bowl whisk together the lime juice and honey until well combined. Coarsely chop the grilled onions and add to the lime mixture, tossing to coat. Add the diced papaya and chopped cilantro and carefully stir to combine. Season to taste with salt and pepper.