Preheat the oven to 375 degrees F. Line a rimmed baking sheet with foil and place the eggplant on top. Use a fork to prick the eggplant 4 times, then place the eggplant in the oven and roast it until it has completely collapsed and a paring knife easily slips into the center, 40 to 50 minutes. Cool the eggplant 20 minutes. Leave the oven on.
Slice the eggplant in half lengthwise and use a spoon to scoop out the flesh (discard the skin). Place the roasted eggplant in a medium bowl and stir in the egg and beans. Add the garlic, basil, parmesan, 3/4 teaspoon salt and 1/2 teaspoon pepper and stir to combine, then mix in the breadcrumbs.
Again, line the rimmed baking sheet with a clean sheet of foil and lightly mist it with spray. Shape the eggplant mixture into balls about the size of a golf ball (2 tablespoons per ball; you should get about 16). Place them on the prepared baking sheet and lightly mist the top of the balls with spray. Bake the eggplant balls until they are golden brown and firm, about 20 minutes.
While the meatballs cook, warm the marinara sauce in a small saucepan. Remove the meatballs from the oven, sprinkle with a little extra parmesan and serve with the marinara sauce.