Garlic béchamel:
Preheat oven to 425°. Salt the eggplant for 30 minutes, then rinse & pat dry. Brush both sides with oil. Set on sheet pans and bake until bottoms are browned, approx. 15-20 minutes. Turn over and bake again until 2nd side is browned, approx, 15-20 minutes. Season with salt & pepper & set aside.
Slowly heat the milk with the garlic in a saucepan. Just before it comes to a boil, cover the pan, turn off the heat & set aside for 15 minutes. Melt the butter in another saucepan over medium heat, add the flour & cook, stirring for 2 minutes. Pour in the milk through a strainer (to remove garlic pieces) & stir until thickened. Cook over very low heat for 20 minutes, stirring occasionally. Remove from heat & add the cream & salt & pepper to taste.
Lightly butter an 8x10 inch baking dish. Spread ½ cup sauce on the bottom. Add a layer of noodles and cover with 1/3 cup sauce. Lay down 1/3 of the eggplant, cover with 1/3 of the mozzarella, 2 tbsp parmesan & 1/3 of the basil. Repeat with 2 more layers. Top with noodles, the remaining sauce & remaining parmesan. Cover with foil & bake at 400° for 25-30 minutes. Remove the foil and bake for an additional 15-20 minutes. Let sit for 10 minutes before serving.
Serves 6-8