Cut the eggplants into slices about a quarter of an inch thick. The shape is really irrelevant; it’s the thickness that really matters. Place the eggplant slices in a bowl. Toss with the olive oil, thyme, salt and pepper.
Heat a heavy skillet (I used a cast iron pan), brush the bottom with a little olive oil, and grill the eggplants until lightly charred and just done (see tips).
Arrange the eggplant slices, slightly overlapping, on two heat-proof plates.
Divide the tomato sauce into two portions and pour over the eggplants. Top with grated cheese.
Broil at 475F, about six inches from the heat just until the cheese is bubbly and lightly browned.
Serve the eggplants hot accompanied by bread, rice or pasta.