Eggplant Meatball Casserole

eggplant (1 pound), stemmed and cut in 4 3/4-inch planks

Coarse salt and freshly ground pepper

fresh breadcrumbs, preferably from a hearty Italian loaf

extra-virgin olive oil

grated Parmesan cheese (1 1/2 ounces)

small garlic clove, minced plus 2 cloves thinly sliced

large egg white

whole plum tomatoes, pulsed in food processor

Red pepper flakes

mozzarella cheese, sliced into 12 thin squares