Make the choux. Put the milk, water, butter, salt and sugar in a large, deep sided, pan. Bring to the boil until butter is completely melted.
Take off the heat and add all the flour at once. Stir vigorously with a spatula until the flour is fully incorporated.
Put the pan back on the hob and keep stirring over medium heat until the dough comes away from the edges of the pan – 2-4 minutes.
Break the eggs into a measuring jug and lightly combine with a fork. Put the dough in the bowl of your stand mixer and mix using the paddle attachment to release some of the steam.
Slowly add the eggs while mixing at medium speed. The pastry will separate and become shiny with each egg addition but will come back together after beaten.
Before you add all the eggs, check the consistency by lifting some of the pastry with a spatula. It should form a peak still attached to the spatula. I usually end up with a little egg leftover which I use as egg wash. Cool for 10 minutes.
Preheat the oven to 200C | 400F. Line a large tray with baking parchment.
Transfer the pastry into a piping bag fitted with a large open star nozzle (or a plain one). Pipe rings as shown here or for small puffs pipe about 1 tbsp of choux pastry on the prepared tray forming a little mound of about 5cm (2in) diameter.
Gently flatten the tops of the choux with a pastry brush dipped in the leftover egg.
Bake for 15 minutes without opening the door. Lower heat to 190C (375F) and bake for a further 15 minutes or until crisp, risen and golden.
Turn the oven off. Take the tray out and pierce the sides of the choux with a knife to release some steam. Return to the (turned off but still warm) oven until crisp. If the choux still look limp rather than crisp turn the oven on to 150C (300F) and bake with the door slightly ajar until crisp. Cool completely before filling.
Make the filling. Finely chop the chocolate and put in a bowl.
Put the double cream and vanilla in a small saucepan and heat until small bubbles appear around the sides of the pan – just before it comes to the boil.
Pour over the chopped chocolate and leave for 5 minutes.
Use a balloon whisk to gently combine the cream and chocolate (which should have melted) into a glossy ganache. Cover and chill for 30 minutes.
Whisk the cooled ganache with 2 tbsp caramel until it forms firm peaks. Transfer to a piping bag fitted with a large star nozzle.
Use a serrated knife to slice the choux rings in half, removing any undercooked dough. For the puffs, make a small hole on the bottom of each. Fill with the ganache.
Drizzle with the caramel (heat gently until runny if needed) and sprinkle with the chopped hazelnuts. Serve immediately.