Prepare two batches of pie dough or a single batch of puff pastry dough according to recipe instructions and then chill as indicated before beginning. If using store-bought: allow to thaw according to package instructions.
Preheat oven to 400F (200C).
Remove dough from refrigerator, remove from wrapping, and turn it out onto lightly floured surface (if I am using homemade dough I work with just half at a time, keeping the second half in the refrigerator. If using store-bought puff pastry, work with just one sheet at a time).
Use a rolling pin to roll to ⅛", and neatly cut dough into 4.5" squares (I like to use a pizza cutter or a knife and a ruler). Transfer to a parchment-paper-lined baking sheet (you will need to gather the scraps and re-roll them out to make all 10 turnovers).
Add your vanilla extract to your melted butter and stir. Use a pastry brush to brush the center of each square with butter (leave about a 1" perimeter unbrushed).
Place chopped chocolate in a microwave-safe bowl and heat in 20-second intervals until completely melted. Add heavy cream and stir until smooth.
Chocolate mixture will be thick. Scoop by approximately 1 ½ Tablespoon-sized scoops and dollop the chocolate slightly off-center into the square. Slightly flatten with your fingertips if the dollop is too tall.
Carefully fold one corner of each square over to the other to cover the chocolate filling, and use the tines of a fork to seal each turnover.
Make an egg wash by beating together egg and teaspoon of water. Brush lightly over each turnover and sprinkle with sugar, if using. Cut small slits across the top of each triangle to vent.
Bake on 400F (200C) oven for 20 minutes, or until turnovers are lightly golden brown.
If desired, create chocolate glaze by whisking together sugar, cocoa powder, milk, and vanilla extract until smooth. Drizzle over turnovers.
Allow to cool on pan before enjoying (chocolate can be extremely hot!).