Baked Eggplant Parmesan

plus 2 tablespoons olive oil, divided

large garlic cloves, minced

San Marzano tomato puree (you can also use whole tomatoes, pureed with juices in blender or food processor until smooth)

, plus more

salt, or to taste

large eggplant, sliced into 3/8-inch thick slices

fresh mozzarella cheese, grated or sliced (3 cups grated)

finely grated Parmesan cheese (1/2 cup grated)