Preheat oven to 350F. Grease 9" x 9" baking pan.
In the bowl of a standing mixer, beat butter and sugar until light and creamy. Add eggs, hazelnut and vanilla extract, mixing until smooth.
In a separate bowl, whisk together flour, salt and baking powder. Gradually add to butter mixture and mix until combined. Evenly spread into pan. Bake for about 25 minutes, until edges are lightly browned. Let cool.
In the bowl of a standing mixer, beat the butter on medium speed until smooth. Add cocoa powder and powdered sugar (one cup at a time) and mix until incorporated. Add hazelnut extract and heavy cream, mix until combined. Scrape down the sides and bottom of the bowl with a rubber spatula as needed. Beat on medium-high for another minute until creamy.
Remove cooled cookie from the pan, then frost. Use a cheese grater to shave some chocolate on top. You won't need much! It just adds a fun texture to the smooth frosting. Cut into bars and enjoy!