Preheat the oven to 180°C (350°F) and line a baking sheet with parchment paper.
Cut the aubergines into small cubes and spread them in a single layer on the prepared baking sheet; drizzle with 1 tablespoon extra-virgin olive oil and season with sea salt and black pepper.
Roast the aubergine cubes for about 30 minutes, until very tender, then remove from the oven and let cool for 5 minutes.
Place the roasted aubergine in a large bowl. Add the pine nuts, lemon zest, grated Parmigiano Reggiano, 200 g breadcrumbs, the egg white, chopped basil, and season with salt and pepper.
Mix thoroughly until combined; if the mixture feels too wet, add more breadcrumbs a tablespoon at a time until it holds together into a dense mixture.
Shape the mixture into 10–12 balls about 1 inch (2.5 cm) in diameter, then roll each meatball in extra breadcrumbs to coat and seal them evenly.
Heat 4 tablespoons olive oil in a large frying pan over medium-low heat until shimmering.
Fry the meatballs in batches for about 2 minutes on one side, then turn and cook an additional 2–3 minutes, until golden-brown and crispy on all sides.
Transfer cooked meatballs to a plate lined with paper towels to drain excess oil.
Serve the aubergine meatballs on their own or with warm marinara or Italian tomato sauce.