Preheat the oven to 375 degrees F. Place the flour on a plate.
Heat the oil in a large nonstick skillet over medium heat. Season the eggplant with salt and pepper. Working in batches, coat the eggplant slices in flour, shake off excess, and add to the skillet. Cook until the slices are golden brown on both sides. Drain on paper towels.
Combine the ricotta, 1/2 cup Parmesan, parsley and egg in a medium bowl. Spread 1/2 cup pasta sauce over the bottom of a baking dish. Place several tablespoons of ricotta mixture on the end of an eggplant slice, roll up the slice and place it in the baking dish. Continue with the remaining eggplant.
Top with the remaining pasta sauce and sprinkle with the mozzarella and the remaining 1/4 cup Parmesan. Bake until bubbly, about 30 minutes.