Preheat oven to 450 degrees, with racks in upper and lower thirds. Arrange eggplant on two rimmed baking sheets. Brush eggplant on both sides with oil, and season with salt and pepper. Bake until golden brown and very tender, 20 to 25 minutes, turning slices and rotating sheets halfway through.
Meanwhile, make sauce: Off heat, in a medium saucepan, whisk together 1/4 cup milk, flour, and garlic. Gradually whisk in remaining 3/4 cup milk and 1/2 cup marinara sauce. Bring to a boil; reduce to a simmer, and cook until pink sauce has thickened, 2 to 3 minutes.
Spread 1/4 cup marinara sauce in the bottom of a shallow 2-quart baking dish. Alternate layers of baked eggplant with pink sauce. Dollop with remaining 1/4 cup marinara sauce. Sprinkle with mozzarella and Parmesan. Bake on upper rack until browned and bubbling, 10 to 15 minutes.