Cut the butter into one inch chunks and put into a stand mixer bowl. Using the paddle and on low speed, mix the butter for one minute to soften. With the mixer running, add the sugars and continue on low speed until the sugar is incorporated. Increase the speed to medium-high and beat the mixture until it is smooth and creamy. Stop the mixer and scrape down the sides and bottom of the bowl with a rubber spatula to make sure all of the butter is fully incorporated.
Add the peanut butter and vanilla extract and mix on low speed until the mixture becomes smooth.
Add the eggs one at a time, waiting until the first one is absorbed before adding the next. Once both eggs have been added and the mixture is smooth, stop the machine and scrape down the bowl.
Add the dry ingredients all at once and mix on low speed until the flour is nearly incorporated.
Stop the mixer and add the peanuts. Return the mixer to low and mix until they are evenly distributed throughout the batter.
Using a teaspoon, drop the cookie dough on a parchment or silpat lined baking sheet, about one inch apart.
Chill the dough for 10 minutes, Then before baking, sprinkle the tops of the cookies with granulated sugar and mark with a criss cross pattern using a fork.
Bake for approximately 12 minutes, rotating the pan halfway through the baking time. The cookies should be light golden on the outside, and soft on the inside.