Wash the eggplant and slice it into thin slices. Place the slices in a colander set over a bowl and sprinkle generously with salt. Place a plate or other weight on top to press the eggplant down. Let sit for at least 30 minutes to draw out excess liquid and bitterness.

Rinse the eggplant well under cold water and pat completely dry with paper towels.

Heat the oil over medium-high heat. Working in batches, fry the eggplant slices for 2–3 minutes per side, or until golden brown and tender. Transfer to a paper towel-lined plate to drain.

Preheat the oven to 375°F.

In a 7 x 11-inch ovenproof casserole dish, spread a layer of marinara sauce over the bottom. Add a layer of fried eggplant, followed by cheese. Repeat the layers, beginning with marinara and ending with eggplant. Spoon more marinara over the top and finish with a generous layer of cheese.

Cover with foil and bake for 30 minutes. Uncover and bake for an additional 15 minutes, or until the cheese is melted, bubbly, and lightly browned.

Let rest for a 30 minutes before serving.