Slice the eggplant, zucchini, and summer squash 1/8 inch thick and place in a large colander. Sprinkle a very generous amount of salt over the slices, and toss to coat. Place the colander over the sink and allow the vegetables to sit for 30 minutes.

Preheat the oven to 375°F.

Spray a 9-inch glass pie plate with nonstick cooking spray.

After 30 minutes, thoroughly rinse the eggplant, zucchini, and summer squash slices with cool water. Pat dry with paper towels.

Slice the tomato 1/4 inch thick. Mince the garlic clove.

Arrange the eggplant slices around the outer edge of the pie plate, so that they are propped at a 45° angle. Lay the tomato slices over the eggplant, creating concentric circles. Alternate slices of zucchini with slices of summer squash over the tomatoes.

Sprinkle the minced garlic over the vegetables, followed by the thyme, grated Parmesan, and sharp cheddar.

Bake on middle rack of oven until the vegetables are tender and the cheese is melted and golden, 30-35 minutes.

Check to see that vegetables are done. Remove from oven or add time as needed.

Allow the vegetables to cool for 5-10 minutes. Plate and serve.