Meanwhile, put the garlic cloves on a sheet of heavy-duty foil and drizzle lightly with olive oil. Wrap the garlic in the foil. Spread the eggplant slices on a large rimmed baking sheet and brush both sides generously with olive oil. Roast the eggplant and the garlic in the lower third of the oven for 45 to 50 minutes, until the eggplant is very tender and browned on the bottom and the garlic is very soft. Using a thin spatula, loosen the eggplant from the pan, then cover with foil and keep warm. Peel the garlic cloves.