Whisk together the vinegar, oil, and oregano and brush on the cut sides of the eggplants. Sprinkle with salt and pepper. Preheat a gas grill to high; adjust the heat to medium after 15 minutes. (If cooking over charcoal, allow the coals to burn until they are covered with gray ash.) Grill the eggplants cut-side down until browned, about 5 minutes. Flip the eggplants and top each half with a slice of provolone. Grill 3 minutes more or until the cheese is bubbly. Top with some Grilled Salsa.
Rainy-Day Method: Prepare the eggplants as described above. Heat the broiler and cook the eggplants about 6 inches from the heat, cut-side down, for 5 minutes. Turn and broil cut-side up for about 3 minutes. Add the provolone and broil about 3 minutes more.