Put the flour, cocoa, sugar, baking powder, salt and butter in a freestanding electric mixer with a paddle attachment (or use a handheld electric whisk) and beat on low speed until you get a sandy consistency and everything is combined.
Slowly pour the milk into the flour mixture, beating well until all the ingredients are well mixed. Add the egg and beat well (scrape any unmixed ingredients from the side of the bowl with a rubber spatula).
Spoon the batter into the paper cases until two-thirds full and bake in the preheated oven for about 20 mins, or until the cake bounce back when touched. let the cupcakes cool slightly in the pan before turning out onto a wire rack to cool completely.
When the cupcakes are cold, hollow out a small section in the center of each one and fill with a dollop of Nutella and cover it with the cut put piece.
Icing Preparation
Beat the icing sugar and butter together in a freestanding electric mixer with a paddle attachment (or use a handheld electric whisk) on medium-slow speed until the mixture comes together and is well mixed. Turn the mixer down to a slower speed. Slowly pour in the milk, then when it is all incorporated, turn the mixer up to high speed. Continue beating until the frosting is light and fluffy, at least 5 mins. The longer the frosting is beaten, the fluffier and lighter it becomes.
Stir in the Nutella by hand until evenly mixed into the frosting. When the cupcakes are cold, spoon the frosting on top.
Notes
I got 12 std size cupcakes with the above qty. I baked @ 180 C, for 17 mins. The oven time varies for each oven, so have monitor it closely after first 15 mins of baking. I used low fat milk. I used a piping bag to fill the cupcakes with Nutella. You can store the cupcakes with frosting @ room temp for 2 days and without frosting @ room temp for 3-4 days. Frsoted cupcakes can be stored in the fridge for 2-3 days. Just leave it outside for 10-15 mins before serving.