Preheat oven to 350°F. Grease a standard sized donut pan and set aside.
In a large bowl, mix together flour, cocoa powder, brown sugar, spices, baking soda, baking powder, and salt. Set aside.
In a small bowl, whisk egg, milk, vegetable oil, vinegar, and vanilla extract. Add the wet ingredients to the dry, whisking to combine.
Transfer mixture into a pastry bag or large ziplock with a hole cut into the corner. Pipe batter into donut molds, filling 2/3 of the way up the molds. Bake for 12 minutes, or until a knife inserted into the donut comes out clean. Allow to cool slightly before frosting.
While the donuts are cooling, make the frosting. In a microwave-safe bowl, combine the chocolate and the butter. Whisk in the corn syrup, powdered sugar, heavy cream, vanilla extract, and cinnamon. Dip each donut into the frosting and top with chopped chocolate.