Cream the butter and granulated sugar until well incorporated. Add the egg and vanilla, scraping when necessary. Sift together the whole-wheat flour, cocoa powder, baking powder, and salt until all the lumps disappear. Add the sifted mixture to the butter mixture, and mix on low speed until well incorporated, scraping when necessary.
Divide the dough in half, wrap, and refrigerate for 1 hour.
Once the dough is chilled, preheat the oven to 350F, and line a baking sheet with parchment paper. Roll out the dough onto a lightly floured surface until about 1/8- to 1/4-inch thick.
Cut the shape of your choice (I chose to use a small biscuit cutter), and bake for 10 to 13 minutes until set.
Once the cookies are baked and cooled, begin to prepare the filling.
Combine the butter, half and half, vanilla, and salt until well incorporated. The mixture will be lumpy, so scrape often.
Add the sifted powdered sugar, scraping often, and mix on low speed until well incorporated. The mixture will be a bit stiffer than cake icing.
Once incorporated, transfer the mixture into a piping bag if making a large batch of cookies. If making a few cookies, like I did, I like to use a small offset spatula to fill the cookies.
You can freeze the extra filling for later use if need be. Just pop into a zip-top bag, and bring to room temperature naturally when ready to use. Or save it in a glass jar for up to 30 days in the fridge.