Slice the eggplant, layer in a colander and salt all the slices. Let the salted eggplant sit in the colander for at least 30 minutes to release the water. This is critical because if you don’t your eggplant will soak up oil when you fry them. Rinse the salt off the slices and pat dry with a towel or paper towel.
Add flour and salt and pepper to taste to a dish for dredging. Dredge each slice in the flour. In a large skillet add oil and heat to medium high. Add the pieces to the oil in batches, cooking until golden brown on both sides. You may need to add a little oil, as they will absorb the oil, the reason why the salting ahead of time is crucial. When browned, remove and drain on a rack or on paper towel.
Layer your cooked slices on a sheet pan large enough to hold all of them in one layer. Top them with very thinly sliced onion. I just layer with pieces, not an entire slice. Top with the grated cheddar cheese. Bake for about 5 minutes at 400 degrees until Cheese has melted!