Using a food processor or box grater, grate 1-2 small zucchinis. Wring out excess water and set aside. Line muffin tins with paper liners and set aside.
Stir butter, oil, sugar, vanilla, egg and sour cream in the bowl of a stand mixer using the paddle attachment until light and fluffy. Slowly incorporate dry ingredients. Scrape sides of bowl and stir again to ensure even mixing. Stir in grated zucchini and chocolate chips.
Scoop into lined muffin tins 2/3 full and bake at 350 degrees for 17-20 minutes or until completely cooked.
Once cupcakes come out of the oven, melt butter, chocolate syrup and milk together in a small saucepan over medium low heat. Once butter has melted and mixture has come to a light bubble, remove from heat and whisk in vanilla and powdered sugar until smooth. Spoon over warm cupcakes and top with sprinkles if desired. Serve.