Marinated and grilled eggplant: slice eggplant into 1/4-inch half circles.

Lightly salt the eggplant slices and place them in a colander or on top of paper towels. This will help remove some of the moisture in the eggplant. Allow the slices to sit for 30 minutes.

While the eggplant is resting, combine olive oil, soy sauce, brown sugar, rice wine vinegar, garlic, ginger, parsley, and sliced pepper or red pepper flakes in a medium-sized bowl and whisk to combine fully. This is your marinade. Once 30 minutes have passed and the eggplant has drained a little, add the slices to the marinade and allow everything to marinate for 30 minutes to 1 hour. 

Grill the eggplant slices for 3 to 4 minutes per side over a medium-high heat grill or grill pan. Remove the eggplant from the grill and store in the refrigerator for up to five days. 

Dressing: combine vegetable oil, sugar, vinegar, parsley, salt, pepper, and hot sauce in a jar with a lid. Cover with lid and shake to mix well. This will make more dressing than you need, but it works well on a salad and should keep in your refrigerator for a few weeks.

Sandwich assembly: slice your six-inch sub roll to get it ready for the ingredients. Add mayonnaise (if using) to the bottom roll. 

Top with slices of eggplant and then cover those with mozzarella. Add tomato slices and then lightly salt and pepper the tomatoes.

Toss shredded lettuce in a small bowl with 2 to 3 tablespoons of dressing and then cover the tomato slices with the dressed lettuce. At this point I usually will drizzle another tablespoon or 2 on the inside of the top sandwich roll as well, just to give the sandwich some extra moisture. 

Cover and close the whole sandwich with the top of the roll and serve.