In a small saucepan, heat the butter over medium-high heat, stirring regularly. Once the butter has melted, keep heating until it just starts to brown and the fragrance of the butter turns nutty. Remove from the stove and let cool.
Preheat the oven to 325F degrees. Place the rack one place above the middle position.
In a medium bowl, whisk together flour, cocoa powder, baking soda, salt and brown sugar.
In a small bowl, whisk together buttermilk, egg, melted butter, and vanilla extract until thoroughly combined.
Pour the wet ingredients into dry ingredients with a large spoon or spatula. Fold together until all the ingredients are well combined, do not over mix it.
Add the ¼ cup mini chocolate chips and just fold in to spread throughout the mixture.
In filling the doughnut cups of the baking pan, I've found the easiest method is placing the batter in a large plastic bag and cutting a 1" slit off the corner. Then squeeze the batter out the hole into each circle, dividing all the batter among 6 doughnut cavities. Alternately, you can use a small spoon to fill the cups, but this takes longer.
Bake the doughnuts for 9-11 minutes, or until a toothpick inserted into one of the doughnuts comes out just clean. Don't overbake or the doughnuts might be dry.
Remove from the oven and allow to rest for 5 minutes before inverting doughnuts onto a wire rack to cool completely. Allow doughnuts to cool completely before glazing.
To make the glaze, in a medium bowl whisk together powdered sugar, cocoa powder and salt. Add the vanilla extract and 3 tablespoons milk. Whisk to combine. Mixture may be thick. Add more milk as desired, until the glaze is thick but pourable.
Dip each doughnut, bottom side, into the chocolate glaze and return to the wire rack. Sprinkle with nuts or candies if desired.
Allow to rest for at least 2 hours, but 3 is better, before serving to allow the glaze to become super delicious and chocolatey.
Store doughnuts in baking box or lightly covered with foil. I don't recommend storing in a plastic air-tight container as the glaze becomes withery.
Serve within two days of baking.
The doughnuts can be made several days ahead and kept frozen without any glaze until the day of serving.