Preheat oven to 200°C and line a large oven tray with baking paper.
Place eggplant onto prepared tray. Drizzle with EVOO and toss to combine with salt and pepper. Bake for 20 minutes or until browning. Set aside.
To make the sauce, place onion, garlic, chilli and EVOO into the Thermomix bowl and chop 4 sec/speed 6. Sauté 5 min/Varoma/speed 1. Add tomatoes, basil, salt and sugar and cook 10 min/100°C/speed soft.
Meanwhile, cook spaghetti in a large pot of salted boiling water, as per package instructions.
To serve, place spaghetti into a bowl, top with eggplant, sauce, cheeses and basil.
To grate the cheeses, place both into a clean dry Thermomix bowl and mill 10 sec/speed 10.