Toast the pine nuts in a dry non-stick pan, stirring, until golden brown. Leave to cool.
Cut the avocados in half, remove from the stone, peel and cut into thin slices.
Place the avocado slices in rosette-shapes on plates and sprinkle with lemon juice. Plunge the tomatoes into boiling water, then drain, skin, halve, deseed and dice. Place the tomato cubes in a small bowl, season with salt and pepper and mix with 2-3 tbsp olive oil. Scatter the marinated tomato cubes on the avocado slices.
Rub the oyster mushrooms with kitchen paper and trim the stalks. Cut into pieces if large.
Peel and finely chop the onion and garlic.
Heat the remaining oil in a pan and fry the onion until softened.
Add the mushrooms and garlic and cook, stirring occasionally, for 5 minutes.
Drain the basil, shake dry and pick off the leaves.
Spread the fried oyster mushrooms, the toasted pine nuts and the basil leaves on the avocado carpaccio. Sprinkle with the remaining lime juice, season with pepper and serve.