Soak the tapioca in the water for 30 minutes. (see note)
In a saucepan, mix the almond milk, salt and honey together.
Without draining, add the soaked tapioca to the milk and honey.
Over medium flame, bring the mixture just to a boil, whisking very frequently.
Reduce the heat to low and cook, stirring often, for 10 to 12 minutes, until the tapioca has thickened, and the pearls are soft and translucent.
Add the chocolate, stirring to melt.
Temper the yolks by whisking a little of the hot mixture into the yolks. Then whisk the tempered yolks back into the pudding. Cook on low flame, whisking, for about 2 minutes.
In a clean bowl, whisk the egg whites until they form a peak that folds over.
Temper the whites by stirring some of the hot mixture into them, then fold the tempered whites back into the pudding. Cook another minute, gently folding and stirring to incorporate the whites into the chocolate.
Stir in the vanilla and rum, making sure everything is well mixed.
Portion the pudding into individual glasses or cups. You can also serve from one larger dish.
Serve warm or cold. (The pudding thickens as it cools.)
If not serving immediately, cover with pieces of plastic wrap, placing the film directly on top of the pudding to prevent a skin from forming.
Serve with strawberries, if desired.