Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving a little overhang on two sides, or grease it well.
In a large bowl, beat the softened butter and sugar with a hand mixer or wooden spoon until light and fluffy, about 2 minutes.
Add the egg, chocolate milk and vanilla, and mix until smooth.
In a separate bowl, whisk together the flour, cocoa powder, baking powder and salt. Add the dry ingredients to the wet ingredients and stir just until no dry streaks or lumps remain.
Spread the batter evenly in the prepared pan.
Bake for 20 to 25 minutes, until the center springs back when lightly pressed and a toothpick inserted in the center comes out with a few moist crumbs.
Let the cake cool in the pan on a wire rack for about 20 minutes, until it is just warm.
Spread the chocolate hazelnut spread evenly over the warm cake. Sprinkle with the chopped hazelnuts and press them in lightly so they stick.
Let the topping set for about 30 minutes. Lift the cake out of the pan by the parchment and cut into 9 bars.
Notes
Pan size: This recipe is made for an 8x8-inch pan. A 9x9-inch pan works too. The bars will be a little thinner, so start checking them at 18 minutes.No chocolate milk? Regular milk works fine. The bars will taste a little less chocolaty.Stiff Nutella: Microwave the spread for 10 to 15 seconds so it spreads easily.Serving tip: Serve warm with vanilla ice cream and a few chocolate chips on top.Storage: Keep in an airtight container at room temperature for up to 3 days or in the refrigerator for up to 5 days. Freeze individually wrapped bars for up to 3 months.