Preheat the oven to 350 degrees F (175 degrees C). Grease two 12-cup muffin tins or line cups with paper liners.
Beat brown sugar and eggs together in a bowl with an electric mixer until thick and pale, about 10 minutes; beat in oil and melted chocolate until incorporated.
Whisk flour, baking powder, baking soda, and salt together in a separate bowl; stir into brown sugar mixture until just blended. Stir in zucchini and ½ cup walnuts until evenly distributed.
Divide batter among the prepared muffin cups, using an ice cream scoop, filling each ⅔ full.
Bake in the preheated oven until a toothpick inserted into centers comes out clean, about 20 minutes.
Cool in the pans for 10 minutes. Transfer cupcakes to a wire rack to cool completely, 20 to 30 minutes more.
Spread frosting over cooled cupcakes; garnish with remaining ¾ cup walnuts.
