Step 1: Preheat the Oven

• Preheat your oven to 375°F (190°C).
• Lightly grease a 9×13-inch (23×33 cm) baking dish with olive oil or non-stick spray.

Step 2: Prepare the Vegetables

1. Thinly slice the eggplant and zucchini using a mandoline slicer or a sharp knife.
2. Lay the slices on a clean kitchen towel or paper towels and sprinkle with salt to draw out moisture. Let them sit for 10 minutes.
3. Pat the slices dry with another towel to remove excess moisture.

Step 3: Make the Cream Sauce

1. Heat the olive oil in a medium saucepan over medium heat.
2. Add the minced garlic and sauté for 1 minute until fragrant.
3. Stir in the heavy cream, thyme, salt, black pepper, and a pinch of nutmeg.
4. Cook the sauce for 2-3 minutes, stirring occasionally, until it thickens slightly. Remove from heat.

Step 4: Layer the Gratin

1. Arrange a layer of eggplant slices on the bottom of the prepared baking dish.
2. Drizzle one-third of the cream sauce over the vegetables. Sprinkle with one-third of the Parmesan and mozzarella cheeses.
3. Repeat the process with the zucchini slices, alternating layers, and finish with a final layer of cheese on top.

Step 5: Bake the Gratin

1. Cover the baking dish loosely with aluminum foil.
2. Bake in the preheated oven for 30 minutes.
3. Remove the foil and bake for another 15-20 minutes, or until the top is golden brown and bubbly.

Step 6: Rest and Serve

1. Let the gratin rest for 5-10 minutes after baking to allow it to set.
2. Garnish with additional fresh thyme if desired. Serve warm as a main dish or side.