Use a pan wide enough to hold two cups/ramekins and part fill it with water so that it comes half way up the cups/ramekins. Bring it to a boil.
Lightly whisk the egg so that it breaks up but doesn't get too much air in it. Add the dashi, soy, sake and salt and mix together.
Prepare the cups or ramekins with the fillings - split the shrimp in half through the middle and put the two pieces in the bottom, top with a couple slices of mushroom then the carrot slices. (If you like, you can use vegetable cutters to make the carrots into a flower shape.)
Strain the egg mixture over the fillings, letting the carrot slices float to the top.
Put the lids on the cups, if they have them, or cover with foil. Reduce the heat of the pan so that it is just simmering and carefully add the cups/ramekins.
Leave the custards to cook over a low heat for around 10-15 minutes until the custard is fully set. You can eat them warm or cold, as you prefer.