This is a lot like an eggplant Parm but the creamy, cheesy sauce takes you in a different direction than the more classic acidity of tomato sauce. Make and bake in advance, refrigerate and serve the next day for best results.
Technique tip: Bread the vegetables and let them chill in the fridge for an hour or to help the breading adhere better.
Swap option: Don't like eggplant? Use spaghetti squash or rutabaga in its place. You can also make this with layers of pasta (for a more classic version) instead of the vegetables.
Special equipment: One 11- by 17-inch ovenproof baking dish.
For the béchamel sauce:
In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook, stirring constantly, until you smell the flour and butter cooking, 2 to 3 minutes. Do not allow it to brown. Add the milk, garlic, bay leaf and red pepper flakes, and cook over medium-low heat, stirring from time to time, until the mixture thickens, 8 to 10 minutes. Season to taste with salt. Transfer to a bowl to cool.
For the vegetables:1.
In a medium bowl, whisk the eggs with a splash of water. In another medium bowl, combine the breadcrumbs with the garlic powder and oregano. Dip both sides of each eggplant slice in the egg mixture and then in the breadcrumbs. Arrange them in single layers on 2 baking sheets. Bread the zucchini slices in the same way.2.
Preheat the oven to 425 F.3.
In a large skillet, pour enough oil to accumulate about 1/2 inch in the bottom. Heat the oil until it begins to smoke, then use a pair of kitchen tongs to add a single layer of the eggplant to the pan. Cook them 2 to 3 minutes on each side or until golden-brown. Remove from the oil and transfer to a baking sheet fitted with a kitchen towel. Season with salt.4.
Reheat and replenish oil before adding another batch of eggplant to the pan. Repeat the same process with the zucchini.
In an 11- by 17-inch baking dish, remove the bay leaf and spoon about 1/3 of the béchamel sauce on the bottom. Top with a mixed layer of the eggplant and zucchini. Top with about 1/4 of the mozzarella slices and 1/3 of the Parmesan cheese. Arrange 1/3 of the tomatoes on top. Repeat the layering 2 more times to make 3 layers. Top with the remaining mozzarella.
Place the dish on a baking sheet in the top half of the oven. Cook until hot all the way through, 40 to 45 minutes. Run the dish under the broiler for 1 to 2 minutes just before serving for a bubbly, cheesy top. Drizzle with the balsamic.