Preheat the oven to 350°F and line a baking sheet with parchment paper.
Using a hand mixer or a stand mixer fitted with a paddle attachment, cream together the softened brown butter and creamy peanut butter until fully combined and smooth.
Then add in the brown sugar and granulated sugar and cream until light and fluffy.
Add in the eggs and vanilla and beat until just combined.
Add in the flour, baking powder, and salt and mix until fully incorporated.
Then fold in the chopped peanuts. The dough should be sticky.
Scoop half the dough onto one side of baking sheet and pat it into a 10 inch x 2 inch rectangle that’s about 1 inch thick (lightly wetting your hands helps a lot with this step). Repeat with the other half of the dough.
Bake at 350°F for 20 to 30 minutes, until golden brown all over. Remove from the oven and let cool for 25 to 30 minutes. Reduce the oven temperature to 325°F.
Carefully transfer the logs to a cutting board and use a spray bottle filled with room-temperature water to very lightly spritz them (just one spray on each section of the logs). Wait about 5 minutes before using a very sharp serrated knife to slice biscotti ½ inch wide.
Return the peanut butter biscotti slices to the baking sheet, standing them up with ½ inch in between them, so air can circulate around them. Bake for another 25 to 30 minutes, until dry and golden.
Remove from the oven and transfer to a wire rack to cool to room temperature.
Peanut Butter Frosting
In a small bowl, cream together the peanut butter and powdered sugar until smooth.
Then slowly add in the milk until the frosting reaches a smooth, pipable consistency.
Transfer to a piping bag fitted with a small tip (or a ziploc bag with the corner cut off), and pipe the frosting on one side of the biscotti. Then sprinkle with some extra crushed peanuts if desired.
For best results, use processed peanut butter like Jif or Skippy that doesn't separate. Natural peanut butter has too much oil and will negatively affect the recipe.Store biscotti in an airtight container at room temperature for up to 2 weeks.To freeze biscotti: I recommend freezing the biscotti after the first bake. After the biscotti are sliced, freeze in an airtight container for up to 3 months. To finish baking, let thaw and then bake for 25 minutes as normal.Brown the butter: In a small saucepan, melt butter over medium heat. Once melted, stir frequently and watch closely for the formation of brown specs on the bottom of the pan and a nutty aroma. Once you see brown specs, stir for just a few more seconds (it browns super quickly). Remove from the heat and immediately pour into a different bowl to prevent it from burning. Let cool to room temperature. I recommend making the brown butter the night before you make the biscotti, so that it has time to fully cool to room temperature! 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.