Preheat oven to 375°F. Place an oven-safe rack over a large rimmed baking sheet covered with foil. Lightly spray rack with cooking spray.
Combine bread crumbs, Parmesan, 1/4 tsp. each of the salt and black pepper in a wide-rimmed bowl. Place egg and 1 Tbsp. water in a separate bowl; whisk to combine.
Dunk each slice of eggplant in egg mixture followed by breadcrumb mixture, pressing to adhere. Place eggplant slices on prepared baking rack. Lightly coat eggplant slices with cooking spray. Bake at 375°F for 30 to 35 minutes, rotating pan once halfway through.
Heat oil in a large nonstick skillet over medium. Add shallots and garlic; cook 2 minutes, stirring occasionally, until softened. Add tomatoes, vinegar, tamari, sweetener of choice, and remaining 1/2 tsp. salt and 1/4 tsp. black pepper. Simmer over medium heat 10 to 12 minutes, until mixture reduces and thickens. Remove from heat and stir in 1 Tbsp. of the tarragon.
Combine mayonnaise and remaining 1/2 Tbsp. tarragon in a small bowl; stir well.
To assemble sandwiches, divide eggplant evenly among the bottom half of 4 sliced baguette rolls. Top each with 1 slice mozzarella cheese. Broil bottom half of sandwich for 1 to 2 minutes, until cheese melts. Spread mayonnaise mixture evenly onto other half of each baguette. Top each sandwich evenly with tomato-tarragon relish and lettuce, if desired.