Remove the oregano from the stems by running your fingers down the center branch, and then chop finely. Chop the ends off of the garlic cloves and smash with the flat side of a chef's knife to remove the skin, then chop finely. Heat 2 tablespoons of olive oil over medium-low heat in a small saucepan (careful not to make the heat too high or the ingredients will burn). Add the oregano first and let it cook for about a minute or less, then stir in the garlic. After about 15 to 30 seconds, turn the heat to low and pour in the full can of tomato sauce, letting it bubble for a few minutes. The sauce does not need to cook down. Cover and set aside. Optional: add a glug of dry red wine.
Start heating the oil to 350°F/180°C (about medium heat) while prepping the eggplant. Slice the eggplant crossways into even steaks (thicker slices change cooking time). Pour the flour into a large bowl or zip-top bag and toss the eggplant slices in the flour to coat evenly, knocking off excess. Beat the eggs into a bowl and dip the slices to coat, letting them soak a few seconds per side before letting excess egg drip off. Finally, toss the slices in the panko (or bread crumbs), adding it a little at a time to avoid clumping. Stack the finished slices aside.
Use a thermometer to check the oil temperature is at 350°F/180°C — too high burns the panko before the eggplant cooks, too low leaves it soggy. If no thermometer, test with a small end piece: the oil should bubble rapidly and the slice should take a minute or two per side. Fry until golden-brown. Line a cooling rack with paper towels and place the cooked slices there to set. Season with salt and move the hot oil outside to cool safely.
Set your broiler on high, and slice or grate the mozzarella and Parmesan cheese. Place the fried eggplant slices in a baking dish and top with the cheese (adding cheese before sauce protects the panko crust and gives a better texture). Put them in the oven and keep an eye on them; take them out when the cheese is browned to your liking.