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Preheat the oven to 350°F (175°C), or 160°C fan. Grease a donut pan well.
Banana mixture: In a bowl, whisk together the brown sugar, mashed bananas, warm milk, melted butter, egg, and vanilla until combined.
Flour mixture: In another bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and chopped chocolate.
Combine: Add the banana mixture to the flour mixture.
Stir gently just until combined to form a thick batter.
Spoon or pipe the batter into the donut pan, filling each donut mold about ¾ full.
Bake for 12–15 minutes, or until a toothpick inserted into the donuts comes out clean.
Leave the donuts in the pan for 5 minutes, then loosen the edges with a small spatula before transferring to a wire rack to cool completely.
For the glaze, whisk together the powdered sugar and milk until smooth.
Dip or drizzle the glaze over the cooled donuts, then sprinkle over the fine chocolate pieces.
Storage
Room temperature: In an airtight container at room temperature for up to 2 days.
Refrigerate for up to 3–4 days. If refrigerated, bring the donuts to room temperature for a few minutes for the softest texture.