Preheat the oven to 200 C / Gas 6. Wrap the 4 aubergine halves in foil and place on a baking tray. Bake for 30 minutes. Keep the oven hot.
Cool and unwrap the aubergines; scoop the flesh out with a spoon and place in a colander. Discard the skin. Push down on the the aubergine flesh to get rid of as much excess liquid as possible.
Transfer the aubergine into a large bowl. Add eggs, cheese, breadcrumbs, salt and mint leaves. Mix well until smooth. If too soft, add some more breadcrumbs.
Line a baking tray with parchment and brush with some oil. Wet your hands, take a small piece of aubergine mixture and roll between your palms to form a ball about the size of a walnut. Tuck a cube of Asiago cheese inside the aubergine ball and roll again to secure the cheese inside. Place on prepared tray and repeat with remaining mixture.
Bake in the preheated oven for 20 minutes or until golden brown, turning them gently with a spatula so they cook evenly on both sides. Serve warm.
Aubergines are full of water and very soft once cooked. Therefore, the balls will be much softer than regular meatballs or other vegetable balls. Add more breadcrumbs to make them stiffer.