Preheat the oven to 350°F (177°C) and lightly grease a doughnut pan.
In a large bowl whisk together the flour, dark brown sugar, salt, cocoa powder, and baking powder until evenly combined.
In a separate bowl whisk the egg, melted butter, peanut butter, milk, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and fold gently until just combined; do not overmix.
Spoon batter into the prepared doughnut pan, filling each cavity about three-quarters full.
Press one chopped mini peanut butter cup (4 pieces) into the top of each donut and gently cover with a little extra batter.
Bake for 10–11 minutes, until the donuts spring back when lightly pressed; avoid overbaking.
Let the donuts cool in the pan a few minutes, then transfer to a cooling rack to cool completely.
To make the ganache, place the dark chocolate chips in a heatproof bowl. Heat the heavy cream in a small saucepan until it just begins to simmer, then remove from heat.
Pour the hot cream over the chocolate chips and let sit for 2 minutes, then stir until smooth and melted.
Dip one side of each cooled donut into the ganache, return to the cooling rack, and immediately sprinkle or press additional chopped mini peanut butter cups onto the wet ganache.
Allow the ganache to set briefly before serving.