Preheat grill: Heat grill to high (about 400 ºF [200 ºC]). We want short cooking at high temperature to get grill marks without the vegetables turning mushy.
Make seasoning: In a small bowl mix garlic, oregano, pepper, 1 teaspoon of salt, vinegar, and oil. Stir to combine.
Season vegetables and bread: Brush all the vegetable slices with the seasoning. Use the remaining seasoning to brush the inside of the bread loaf halves.
Grill vegetables: Grill the eggplant 2-3 minutes on each side to get grill marks and slightly soft, but not mushy (we want a somewhat meaty texture). Grill the onions and tomatoes 1 to 2 minutes on each side, until you have some grill marks, but they're still somewhat firm.Place the bread, the inside towards the fire, and heat until they have grill marks.
Assemble: Place an equal number of basil leaves on four of the bread loaf halves. Top with the grilled vegetables, and then the remaining bread. Serve alongside avocado mayo and extra salt and pepper so each person adds them to their taste.