Slice eggplants into 1/3″ thick rounds and sprinkle salt on both sides. Let them sit on the counter for 45 minutes. Pat dry with paper towels. The longer you "sweat" the eggplant, the less oil it soaks up while cooking which is important because this dish is a bit on the oily side. While the eggplant is "sweating" on the counter, start your sauce (see below)
Heat a deep, heavy bottomed skillet or a dutch oven over medium/high heat. Add enough oil to cover the bottom of the pan. Once the oil is hot, arrange eggplant on the skillet and fry about 2 minutes per side. Caution: wear and apron and your cooking mitts and make sure babies have cleared the area (this is a time of substantial oil fireworks).
Remove cooked eggplant to a pyrex dish (you may place it on paper towels to soak up excess oil). Add more oil to the skillet between batches as needed.
How to make Red Pepper Sauce
Grate 3 red bell peppers and 1 jalapeno (use a food processor with a grater attachment if you have one).
In a medium sauce pan mix grated bell peppers, jalapeño, 5 pressed cloves of garlic, 1 tsp salt, 1 Tbsp sugar, 1/4 tsp pepper, 1/3 cup vinegar, 1/3 cup olive oil, and 1/2 cup water . Simmer sauce uncovered for 40 minutes (stirring occasionally). Add more sugar and water to taste in the end.
Assembly and Finishing Touches:
Add 1/2 eggplant slices to 9×13 or 9×12 casserole dish then top with 1/2 red pepper sauce. Repeat with remaining eggplant slices and pepper sauce.
Sprinkle the top with freshly grated parmesan cheese and place the dish in the oven on broil for 3 minutes to melt the cheese.