Line a baking sheet with baking paper and sprinkle with a thin layer of sea salt. Halve the aubergine lengthways and place the cut side down on the salt. Bake in the oven at 200 ° C for 20 minutes.
In the meantime, break through the lasagne sheets in the middle and briefly pour boiling water over them to soften them a little. Cut the shallot into fine cubes and fry in a little olive oil together with the halved cherry tomatoes.
Take the eggplant out of the oven and remove the inside with a spoon and cut into small pieces. Add the pieces to the pan, fry them a little and season with pepper and a little salt (not too much salt, because that was already on the baking sheet and has been pulled into the aubergine).
Now layer the lasagna in a small baking dish and alternately layer the aubergine mixture and the cherry tomatoes between the lasagna sheets. Spread the goat cheese on top.
Bake at 200 ° C (top / bottom heat) for about 10 minutes, until the cheese has melted and the lasagne plates have become a bit crispy. Drizzle with a little olive oil and garnish with the basil.