Aubergine parmigiana lasagne

Name: Aubergine parmigiana lasagne
Ingredients: 3 large aubergines trimmed and thinly sliced lengthways; 4 tbsp olive oil; 250g vegetarian mozzarella drained and coarsely grated; 50g vegetarian Italian-style hard cheese grated; 1 bunch of basil leaves picked and roughly chopped, plus extra to serve; 8 dried lasagne sheets (egg lasagne sheets are best for this); 2 tbsp olive oil; 6 garlic cloves finely sliced; ¼ tsp golden caster sugar; 1 tbsp red wine vinegar; 3 x 400g cans chopped tomatoes