Season the eggplant with salt and pepper. In a wide, shallow bowl, whisk together the eggs and 4 tablespoons pesto. Pour the bread crumbs onto a large plate. Dip each eggplant slice into the egg mixture, then coat with the bread crumbs.
Preheat the oven to 350 degrees ;. In a large nonstick skillet, heat 2 tablespoons olive oil over medium-high heat. Working in batches, cook the eggplant until golden, 2 minutes on each side, using the remaining 4 tablespoons olive oil. Transfer the eggplant to a paper-towel-lined baking sheet.
In a small bowl, combine the ricotta and 3 tablespoons pecorino-romano; season with salt and pepper. Spread 1 tablespoon of the remaining pesto on each eggplant slice and top with about 2 tablespoons of the cheese mixture. Roll up each slice. Bake until the eggplant is tender when pierced with a toothpick, about 10 minutes.
Meanwhile, in a small saucepan, bring the marinara sauce to a simmer. Serve the roll-ups with the sauce and remaining pecorino.