In a separate bowl, whisk together the oil, sugar, pumpkin, eggs, and water.
Add dry ingredients to wet ingredients and mix until just moist.
Prepare muffin tins with paper cups and fill each cup ⅔ full of batter; about 20 cupcakes.
Bake at 400 degrees Fahrenheit for 15 to 18 minutes or until the cake springs back when touched. Allow to cool completely on a wire rack.
Prepare frosting by beating the butter in a large bowl with an electric mixer. Beat in the powdered sugar, salt, and vanilla until smooth. Add the Nutella and beat until light and fluffy. Fill a pastry bag with a large tip full of frosting and swirl on top of cupcakes. Store in an airtight container.