Preheat the Big Green Egg MiniMax grill (or your grill of choice) to 400°. Whisk together the olive oil and Italian seasoning.
Place the sliced zucchini, eggplant, and chayote in a bowl. Drizzle with 1-2 Tbl herbed oil. Gently toss to coat.
Place the veggies on the grill grate in a single layer; grilling for 3-7 minutes per side. You want them tender but not mushy. *Chayote will retain a crispness so if you want grill longer.
Drizzle the tomatoes with some herbed oil and grill for 5 minutes. While grilling, add the hoagie roll, and uncut side down. Flip the tomatoes and place fresh mozzarella on top grilling for 1-2 minutes.
Transfer the hoagie’s bottom part to the plate, and add more mozzarella followed by the tomatoes, grilled zucchini, eggplant, and chayote. Drizzle 1 Tbl of herbed oil over the top. Add the top, slice, and enjoy!