Fold each slice of ham in half and wrap it around the center of a pineapple spear. Heat 1 tablespoon of the oil in a large nonstick skillet over medium heat. Place 10 of the wrapped pineapple spears in the pan. Sear on each side until golden, about 2 minutes. Drizzle 1 tablespoon of the vinegar over the pineapple spears and cook until the vinegar bubbles up and thickens slightly, about 1 minute. Transfer to a plate and cover with foil while repeating the cooking instructions with the remaining ingredients. Serve with the celery stalks, if desired.
Tip: If you're serving the spears as passed cocktail food, wrap them in advance and refrigerate until needed, for up to 6 hours. Cook just before serving.