Line a rimmed baking sheet with parchment paper. Trim the 3 eggplants and slice lengthwise into ¼-inch-thick planks. Arrange on the prepared baking sheet in a single layer and sprinkle liberally with the 1 teaspoon kosher salt. Let stand for 15 to 30 minutes. You should see tiny moisture bubbles on the eggplant’s surface. Meanwhile, arrange a rack in the middle of the oven and heat the oven to 400ºF.

Pat the eggplant slices dry with paper towels to get rid of the moisture and salt. Lightly brush the eggplant with the 1 tablespoon olive oil. Roast until just starting to become pliable, 15 to 20 minutes. Meanwhile, beat the 1 egg in a medium bowl. Add the 15 ounces ricotta, 1 teaspoon dried oregano, ½ teaspoon black pepper, 1 cup of the mozzarella cheese, and ¼ cup of the Parmesan cheese. Stir to combine.

Remove the eggplant from the oven. Reduce the oven temperature to 375ºF.

Spread about ¼ cup of the marinara sauce on the bottom on a 9 x 13-inch baking dish. Arrange about 6 eggplant slices on the sauce (it’s okay if they overlap a little). Dollop ⅓ of the ricotta mixture on top and gently spread it across the eggplant, followed by a thin layer of marinara. Repeat with 2 more layers of the eggplant, ricotta mixture, and marinara. After the final layer of marinara, sprinkle the lasagna with the remaining ½ cup mozzarella and ¼ cup Parmesan.

Cover the baking dish tightly with aluminum foil. Bake for 20 minutes. Uncover and continue baking until the cheese is golden brown and bubbly, 15 to 20 minutes more. Let stand at least 15 minutes before serving. Garnish with parsley if desired.