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Special equipment: a broiler-safe 9-by-13-inch baking dish
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Position 2 oven racks in the middle and upper third of the oven, and preheat to 425 degrees F. Line 2 rimmed baking sheets with parchment.
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Cook the oil, garlic and 1/2 teaspoon salt in a large skillet over medium heat, stirring, until the garlic just starts to turn golden, 4 to 6 minutes.
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Add the tomatoes; rinse the can with about 1 1/2 cups water, and add the tomato water to the skillet.
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Add the kale and basil, bring to a simmer and cook until the sauce thickens, about 25 minutes.
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Meanwhile, combine the almond flour and breadcrumbs in a medium bowl until evenly mixed.
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Whisk the egg whites and 3 tablespoons water in another medium bowl until frothy.
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Lay out the eggplant slices on a clean surface, and season with 1/2 teaspoon salt and a few grinds of pepper.
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Dip the eggplant slices in the egg whites, then press into the almond-breadcrumb mixture to coat.
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Place the eggplant pieces on the baking sheets.
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Bake until the eggplant is tender and the crust is golden brown, about 30 minutes.
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Rotate the baking sheets if the top one is browning too quickly.
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Turn the oven to broil.
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Spread a little of the sauce on the bottom of a broiler-safe 9-by-13-inch baking dish.
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Arrange half the eggplant in the dish in as close to an even layer as you can without overlapping too much.
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Spread half the remaining sauce on top, then 1/4 of the mozzarella.
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Top with the remaining eggplant, sauce and mozzarella and the Parmesan.
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Place the baking dish under the broiler until the cheese is melted and browned, about 1 minute.
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Serve immediately, while the cheese is still warm.
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20
Sprinkle the top with the parsley.
