How to Make It
Preheat the oven to 425°. Brush 3 baking sheets with olive oil. Arrange the eggplant slices on the sheets in 1 layer, season with salt and pepper and drizzle with 1 tablespoon of the olive oil. Bake for about 20 minutes, or until the bottoms are lightly browned; turn and bake for 20 minutes, or until browned on the other side.
In a large nonreactive skillet, heat the remaining 3 tablespoons of oil. Add the scallions and savory and cook over moderate heat, stirring, until softened, 2 to 3 minutes. Add the tomatoes, season with salt and pepper and cook over high heat until slightly thickened, about 8 minutes.
In a small saucepan, melt the Fontina in the cream over moderate heat, whisking until smooth. Season with salt. Remove the pan from the heat, let cool slightly and whisk in the egg.
Spread 3/4 cup of the tomato sauce over the bottom of a 13-by-9-inch baking dish. Arrange one-third of the eggplant slices in the dish, overlapping them only slightly. Pour in one0third of the Fontina cream and sprinkle with one-third of the Grana Padano. Continue layering the tomatoe sauce, eggplant, Fontina cream and Grana Padano 2 more times. Bake for about 30 minutes or until bubbling and lightly browned on top. Let rest 10 minutes before serving.