Preheat oven to 350°F. Grease a standard sized donut pan and set aside.
In a microwave-safe bowl, melt butter and chopped chocolate. Pour into medium sized bowl and stir in brown sugar, egg, milk, and salt. Fold in flour, cocoa powder, baking powder, and baking soda until just combined.
Transfer mixture into a pastry bag or large ziplock with a hole cut in one corner. Pipe batter into donut molds, filling ⅔ of the way up the mold. Bake donuts for 10 minutes, or until a knife inserted in the center of a donut comes out clean. Allow to cool for 10 minutes before frosting.
While the donuts are cooling, make the frosting. In a microwave safe bowl, melt chocolate and butter. Whisk in powdered sugar, heavy cream, corn syrup, and vanilla extract until smooth and shiny.
Once the donuts have cooled, dip one side into the chocolate mixture. Use a spoon to smooth the glaze on the donut. Sprinkle with chopped pistachios. Serve!