Using a stand or hand mixer, cream together the softened brown butter and peanut butter until fully incorporated.
Then mix in the granulated sugar and brown sugar until smooth and creamy.
Add in the egg and vanilla extract and beat for 1-2 minutes until the texture is light and fluffy.
Add in the flour, baking soda, and salt and mix until thoroughly combined. The dough should be wet and sticky.
Gently mix in the chopped peanuts.
Spoon a generous 3 tablespoons of dough and roll into balls. If desired, roll the tops in sparkling sugar.
Cover the dough and chill in the fridge overnight (minimum of 2 hours if you just can’t wait).
Preheat your oven to 350°F and line a light colored baking sheet with parchment paper.
Place dough balls at least 2-3 inches apart on the baking sheet (they will spread, I usually only do 6 cookies on a half sheet pan).
Bake cookies for on the center rack of the oven for 8 minutes. Place a kitchen towel on the counter. Remove from the oven and lightly drop the baking sheet onto the covered counter (only about 2 inches, it's a light drop). This gives the cookies the perfect crackled top.
Return to the oven and bake for another 2-4 minutes are until the edges are fully set and the cookies are light golden brown.
Remove from the oven and let rest on the baking sheet for 2-3 minutes, then transfer to a cooling rack.
Notes
To make brown butter, melt unsalted butter over medium heat, stirring frequently. Watch closely for the butter to develop brown specs and a nutty aroma. Once you start seeing brown specs, let cook for just a few seconds longer (watch very carefully or it will burn). Remove from the heat and pour into a small bowl so that it doesn't continue to cook. Set aside and let cool for about 20 minutes in the fridge until soft and pliable. Note: For every ½ cup (1 stick or 113g), you'll lose about 1 tablespoon (14g) to evaporation while cooking. So you can either add in an extra 1 tablespoon before browning, or if you're browning big batches, just make up the weight difference in your recipe with regular unsalted butter if needed.Store cookies in an airtight container at room temperature for up to 4 days (they'll definitely be gone before then though).Freeze pre-rolled cookie dough balls in the freezer for up to 6 months.