Pre-heat oven to 350 degrees F. Line two muffin pans with paper liners and set aside.
In a medium bowl, mix together the brown sugar, butter, and oil. Beat in eggs, one at a time until well incorporated. Stir in vanilla extract, buttermilk, zucchini, and chocolate chips.
In a separate large bowl, mix together all of the dry ingredients. Add the liquid ingredients and mix until well combined. Spoon batter into large muffin pans, filling them about 3/4 the way full. Bake in the center of the oven for about 30-35 minutes, or until a toothpick comes out clean. Cool cupcakes on a wire rack, while you make the frosting.
To make the frosting, melt the butter. Whisk in the cocoa powder, whisking until smooth. Alternately add powdered sugar and milk, beating to spreading consistency. Add small amount additional milk, if needed. Stir in vanilla. Frost the cupcakes with the chocolate frosting. Decorate with sprinkles, if desired. Store cupcakes at room temperature in an air tight container.
Notes
* Note-the frosting makes about 2 cups, you might have a little extra.