Preheat oven to 350℉. Grease a doughnut pan with non-stick cooking spray or melted butter, set aside.
In a medium bowl, whisk or sift together the flour, baking powder, baking soda, and salt. Set aside. In a large bowl cream together the butter, peanut butter and brown sugar. Whip until creamy, light and fluffy, about 4 minutes. Add the egg and mix until completely incorporated. Stir in the vanilla extract. Add the dry ingredients alternately with the buttermilk, starting and ending with the flour. Do it in three batches, adding flour and mixing until just combine. Then add a splash of the buttermilk and mix once more. Continue in this manner until all the flour and milk has been added. If necessary you can fold in the last bit of the flour to make sure you don't overmix the batter which would result in dry doughnuts.
Spoon the batter into the prepared doughnut pan with a small spoon, filling the pan just a tad shy from the top. Bake in preheated oven for about 8 to 12 minutes or until golden brown and a toothpick inserted comes out clean. Make sure to keep an eye on them because they might be done sooner or might not be done after 10 minutes, depending on your oven. Let them cool in the pan and then transfer the doughnuts to a cooling rack until completely cooled.
In the meantime, make the glaze. Whisk or sift the powdered sugar, cocoa and salt. Start by adding the milk, a tablespoon at a time, whisking until the glaze is not too thick but not too runny. If you need more milk add some a tablespoon at a time. You don't want the glaze runny because it won't stay on the doughnuts and it'll cause the nuts to slide off.
Dunk the doughnuts, rounded side down, into the chocolate glaze and then dip into the chopped nuts. Allow the glaze to set for a bit before eating. Store any leftovers in an airtight container. Best if eaten within two days of making. Enjoy!