Brown Butterfinger cookies: In a medium pan over medium heat, cook entire stick (113 grams butter). Swirl the pan until butter foams up and then finally turns brown. Should take about 5 minutes. 

Once the melted butter has turned brown, remove pan from heat and pour butter into a heatproof mixing bowl. Allow butter to cool for 2 or 3 minutes and then add the small pieces of the second amount of butter (56 grams or 1/2 stick). You want this second amount of butter to melt, but not make any sizzle. That's why you wait 2 or 3 minutes for things to cool off a bit. 

To the mixing bowl with the butter, add sugar and brown sugar and mix to combine until everything is smooth.

Once things are smooth, add egg and egg yolks to butter and sugar mixture. Whisk until everything is fully combined.

Add vanilla extract and whisk to incorporate.  

Add all your dry ingredients at this time (flour, salt and baking soda). Stir and fold everything together until there are no dry, visible spots of flour. 

Chop up all your Butterfinger pieces and add them to the rest of the dough. Try not to over mix. 

Let dough rest for 10 minutes to hydrate everything - this will allow your dough to get firmer and become stiffer so you can work with it better. 

At this point, you can start cooking or you can put your dough into the fridge to firm up even more. I usually will place the dough in the fridge for 30 minutes or up an hour.

When you're ready to bake cookies, pre-heat oven to 350 degrees F (177 C). 

Scoop dough into 2 teaspoon or 1 tablespoon scoops and using your hands, shape the dough scoops into balls and place on a parchment lined sheet pan. Leave at least an inch and a half between each dough ball. They will spread. 

Bake cookies for 9 to 11 minutes.  

Allow to cool on the baking sheets to firm up the cookie. 

Nutella Butterfinger buttercream filling: while cookies are cooling off, add the softened butter and Nutella to a large mixing bowl or the bowl of your stand mixer, mix with a whisk (if by hand) or the whisking attachment of your mixer. Mix until creamy and incorporated. 

Slowly add the powdered sugar to the butter/Nutella mixture. Add the sugar in small amounts and keep whisking between additions so that you will not have lumps and the filling will stay smooth. 

When all the powdered sugar is mixed in, add your chopped up Butterfinger pieces and whisk briefly to fully incorporate. 

Once the filling is fully mixed, add all the filling into a zip top bag or bowl. The zip top bag can be used later as a convenient piping bag which will make things less messy. 

Add filling to the fridge to cool.

Make sandwich cookies: once your cookies have cooled, get the filling out of the fridge and add the filling to a piping bag or zip top bag (if you've already done this, skip to the next step). If you're using a zip top bag, cut a small piece of one of the bottom corners of the bag with scissors or a sharp knife. If you don't have either type of bag, you can use a spoon instead. 

Take one cookie, turn it upside-down and then use your piping/bag to squirt a teaspoon worth of filling onto the upside down cookie. Then take a second cookie and place it right side up on top of the filling. You've now made a cookie sandwich. Repeat until you've made as many sandwiches as you have cookies. 

Store sandwich cookies in a sealed container and eat within 5 days or a week. You can store in the refrigerator, and they should last a bit longer.