Preheat oven to 350F.
Arrange tomatoes on a rack set on a baking sheet and season with salt and pepper. Roast tomatoes 30 minutes.
Place crushed garlic in a small pan with 1/3 cup EVOO. Heat oil to infuse it with garlic flavor then cool.
Meanwhile, preheat a large griddle or grill pan over medium-high heat or preheat broiler to high with rack on the second slot from top of oven.
Brush chicken with garlic oil and season with salt and pepper. Brush eggplant slices with garlic oil and season with salt and pepper. Grill cutlets and eggplant 3-4 minutes on each side. Chicken should be firm and marked; eggplant should be tender and marked.
To assemble, layer eggplant and chicken with mozzarella, roast tomato slices and shaved parm. Place stacks on platter and cover with foil so cheese melts slightly.
Meanwhile, dress basil and arugula with lemon juice and a drizzle of EVOO, salt and pepper, combine with lots of shaved Parm cheese. Serve stacks with basil-arugula salad.