Preheat your oven to 375°F (190°C). Arrange the eggplant slices in a single layer on a baking sheet lined with paper towels. Sprinkle both sides evenly with the kosher salt and let them sit for 20 minutes to draw out excess moisture; pat the slices completely dry with fresh paper towels.
Brush the dried eggplant slices lightly with the 2 tablespoons of olive oil and arrange them on a clean baking sheet. Roast in the preheated oven for 20 minutes, flipping halfway through, until the slices are tender and lightly golden; remove from oven and set aside.
In a medium bowl, stir together the 15 ounces of ricotta cheese, 1 beaten egg, 1/4 cup of Parmesan cheese, and 1/2 teaspoon of black pepper until the mixture is smooth and fully combined.
To assemble the lasagna, spread 1/2 cup of the pesto evenly across the bottom of a 9x13 inch baking dish. Arrange a single layer of 4 no-boil noodles over the pesto, then top with half of the roasted eggplant, followed by half of the ricotta mixture, and 2/3 cup of the shredded mozzarella.
Repeat the layers by adding another 1/2 cup of pesto, 4 more noodles, the remaining eggplant, the remaining ricotta mixture, and another 2/3 cup of mozzarella. Top with a final layer of the last 4 noodles.
Spread the remaining 1 cup of pesto over the top noodle layer and sprinkle with the final 2/3 cup of mozzarella cheese. Cover the dish tightly with aluminum foil.
Bake the covered lasagna for 30 minutes. Then, remove the foil and continue baking for another 15-20 minutes, or until the cheese on top is bubbly and begins to turn golden brown.
Let the lasagna rest, uncovered, on a wire rack for at least 15 minutes before slicing and serving; this allows the layers to set for cleaner slices.