Preheat oven to 220C. Line baking trays with baking paper.
To make pastry: combine chopped butter with 2/3 cup cold water in a saucepan over medium heat. Cook until butter is melted and mixture starts to boil.
Reduce heat to low and add flour. Stir dough constantly to heat evenly for 2-3 minutes until dough forms a coating on the pan (but don't let it burn). Scrape pan to roll dough into a ball and remove from heat. Set aside for 5 minutes to cool.
Reserve 2 teaspoons of egg. Using a wooden spoon, beat in enough egg to make hard peaks but dough should still be quite thick as you do not want mixture to disperse on tray at all when baking. Mixture should be glossy.
Spoon 2-teaspoon balls of dough onto baking trays. Allow enough space between each ball. Brush tops with reserved egg.
Bake for 5 minutes. Reduce oven to 180C. Bake further until golden and puffed (allow at least 5 more minutes). Remove from oven and slice each ball in half, with centers facing upward. Return to oven and bake for 5 more minutes to cook through centres. Allow to cool.
To make chocolate sauce, put chocolate and double cream in a microwave safe bowl. Microwave until chocolate is completely melted, but stop microwave to stir every 30 seconds. Once melted stir thoroughly so that sauce is smooth.
Spoon about a tablespoon of double cream (or Vanilla Bean Double Cream) onto one half of a profiterole and use other half to form a mini sandwich. Continue until all are used. Place profiteroles with cream onto serving plates and drizzle over warm chocolate sauce.