Slice each eggplant in half lengthwise. With a spoon remove the flesh from the center of the eggplant halves, leaving a ¼ inch rim around each. Reserve 100 g of the scooped out flesh.
Place the scooped out eggplant halves on a large baking sheet lined with silicone or parchment paper. Grease them with olive oil (1 tablespoon), inside and outside, season with sea salt. Bake in the oven at 200°C for about 30 minutes until golden. Remove from the oven and set aside.
Chop in a food processor 100 g of the scooped out eggplant flesh and sauté for 5-7 minutes in 1 tablespoon of olive oil, until tender. If necessary, add a little water. Set aside.
Sauté shallots for 4 -5 minutes in ½ tablespoons of olive oil until soft and golden-brown in color. Stir into the tuna mixture.
Sauté cherry tomatoes in ½ tablespoon olive oil in another skillet for about 5 minutes, stirring occasionally, until lightly browned.
Mix and combine chopped eggplant flesh, cherry tomatoes, fried shallots, tuna, capers, salt, pepper, basil and tomato puree.
Stuff evenly the scooped out eggplant halves with the tuna mixture. Top with grated mozzarella, then Grana Padano and finally breadcrumbs. Sprinkle with 1 tablespoon of olive oil. Return to the oven and bake for 10 minutes until the cheese has melted.