Cut top of eggplant. Slice horizontally into 1/2 inch thick slices. Toss with salt and let sit while oven heats up. After sitting for 30 minutes, pat eggplant dry with paper towels.
Arrange eggplant slices, laying flat, on a parchment paper lined baking sheet. Drizzle with olive oil.
Bake for 15 minutes, then remove from oven.
In a shallow baking pan, spread about 1/2 cup marinara sauce on the bottom of the pan. Nestle eggplant slices into pan, it's fine if they are touching.
Put a dollop of marinara sauce onto each eggplant slice. Top with torn muenster slices, then a leaf of basil. Top each stack with another eggplant slice, then spread about 1 cup of sauce over the entire dish. Top with torn muenster slices, to cover the dish.
Bake for 20-25 minutes, until dish is bubbling and cheese is golden brown. Remove from oven and top with more basil and red pepper flakes. Serve.
Leftovers will last for 3 days in the refrigerator.