Mix Nutella and butter together in a stand mixer. Beat until smooth and creamy.
Spoon the powdered sugar into the measuring cup, then level it off with a knife. Don't pack it into the cup.
Add the sugar and vanilla. Beat on medium speed until the mixture is completely combined. The mixture will be very thick, but should be smooth.
Line an 8x8 pan with parchment paper. Press the Nutella mixture down evenly in the pan.
Melt the chocolate chips in a microwave safe bowl very slowly*, about 30 seconds, then stir. Then continue to melt it in 15-20 second intervals, stirring in between until the chocolate is almost melted. Add the softened tablespoon of butter, mix and melt the chocolate an additional 10 seconds if needed. The chocolate should be smooth.
Spread the chocolate evenly over the Nutella mixture. Allow the fudge to set in the refrigerator for about 10 minutes. Remove the dish from the fridge. Pull up on the parchment paper to remove the fudge from the pan.
While the chocolate is still slightly soft, cut the bars**. Place the bars on a cookie sheet and slide them back into the fridge to continue to set for an additional 10 minutes.
Store the bars in an airtight container.
*If you have a "melt" setting on your microwave, set it to chocolate and "8 ounces" and start the microwave. You'll still need to stop the microwave to stir the chocolate every 20-30 seconds so that it does not burn. Be sure that the butter is softened before you add it to the chocolate. It's best to add the butter when the chocolate is 90% melted, then the butter will melt most of the way on its own. Put it in the microwave for an additional 10 seconds, if needed.**When the chocolate hardens completely, it may be hard to cut the bars and not have the chocolate break. I like clean cuts, which is why I cut the bars before the chocolate has completely set. If you forget to do this (which I have done many times!), dip your knife in very hot water before cutting the bars. This will help the chocolate to cut cleanly.