Halve the avocados and discard the pits. Spoon out the flesh and keep the shells.
Place avocado flesh in a bowl and crush with a fork. Season with salt and pepper.
Add the scallions, garlic, lemon, crab meat and mustard. Mix well; reserve.
Next, make the sabayon sauce. In a mixing bowl, add the egg yolks and 4 tbsps of water. Whisk well and place over a pan of boiling water (a bain marie). Whisk energetically for 4 to 5 minutes until the yolks are creamy and foamy.
Fold the sabayon into the avocado mix. Do not cover mix.
Spoon the mixture into the avocado shells. Place them on a baking tray in the oven and cook for 10 minutes. Serve immediately.
When serving the avocados, keep them still by placing them on a small amount of wet salt in the middle of the plate. Serve this with a thick slice of toasted brioche.