You can make this dessert eggless by replacing the eggs with 3 tbsp custard powder or corn flour, directly whisked into the milk mixture and cooked till thick. Pour over the Nutella stuffed bread and bake as usual after the soaking time.
It is not necessary to use chocolate flavored Horlicks! Use any malted drink powder of your choice - Boost, Bournvita, or even normal Horlicks will work.