Cut crosswise into ¼” thick slices to make 12-16 slices. Brush with the oil mixture.
Place on grill over medium-high heat. Close lid and cook, turning and brushing occasionally with remaining oil mixture, until tender (5-10 minutes). Remove from grill. –OR—Cook under the broiler or saute in a frypan until tender, about 4-5 minutes per side.
8 thin slices provolone/Gouda/other cheese
2 tomatoes, thinly sliced
4 large pieces roasted sweet peppers
8-16 leaves fresh basil
Freshly ground pepper
4 crusty rolls or 8 thin slices of crusty bread
Place a slice of cheese on 1 eggplant slice; top with another slice of eggplant. Top with 2 tomato slices or a piece of roasted sweet pepper, then 2-4 basil leaves. Top with third eggplant slice, then another slice of cheese. Top with the 4th eggplant slice.
Repeat to make 4 stacks, adding a grind of pepper at the end if desired. Place on grill, close lid and cook for about 2 minutes.
Drizzle balsamic vinegar on inside of split rolls, or brush the bread with olive oil, toast it on the grill and lightly rub a clove of garlic over the toasted surface (ed.: how exotic!).
Add vegetable stacks and serve immediately. –OR—allow to cool, wrap tightly and refrigerate for several hours, allowing the tastes to blend.