Preheat the oven to 400 degrees F (200 degrees C).
Preheat a grill for medium heat and lightly oil the grate. Grill eggplant slices until cooked through and evenly browned on both sides, about 5 minutes.
Mix half-and-half, egg, ricotta cheese, 1/4 cup Parmesan cheese, salt, and 1/8 teaspoon pepper together in a bowl.
Arrange a layer of eggplant slices in each of 2 individual gratin dishes. Sprinkle each with 1/8 cup Parmesan cheese and season with salt and pepper. Spoon half the marinara sauce into each dish. Top each with a second layer of eggplant slices, more salt and pepper, half the ricotta mixture, and 1 tablespoon Parmesan cheese. Place the dishes on a baking sheet.
Bake in the preheated oven until the custard sets and the top is browned, 25 to 30 minutes.