Spread about 1/2 teaspoon mayonnaise over both sides of eggplant slices using a rubber spatula. Combine crackers and cheese in a shallow dish; dredge eggplant in cracker mixture. Place eggplant in a single layer on a baking sheet coated with cooking spray; chill 2 hours.
Preheat oven to 425°.
Bake eggplant at 425° for 15 minutes; turn eggplant slices over, and bake an additional 5 minutes or until crisp.