Preheat the oven to 350 degrees F. Line 3 baking sheets with parchment paper.
In 10-inch skillet over medium-high heat, heat butter until melted, about 2 minutes. Continue to cook, stirring constantly until butter is dark golden brown and has nutty aroma, 1 to 3 minutes. Remove skillet from heat and let cool slightly.
In a medium bowl, whisk together flour, baking powder and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the eggs until light and pale in color, about 2 minutes. Gradually add the sugar while the eggs are beating. Add the browned butter and vanilla and beat until combined, about 30 seconds. Add the peanut butter and mix until combined. Add the flour in two batches and beat until just combined. Scrape down the bowl and fold in the peanuts, chocolate chips and peanut butter chips.
Divide the dough into thirds and place each portion on a separate baking sheet. Using slightly moistened hands, shape each portion into a log about 15 inches long and 2 inches wide. Smooth the surface of the dough. Bake for 20 to 25 minutes until firm and golden brown along the edges. Let cool on the pan for 10 minutes.
Lower the oven temperature to 325 degrees F.
Using a serrated knife, cut the log into ½-inch slices and set them on the baking sheet cut sides up. Bake for 8 minutes. Flip the cookies over and bake 8 minutes more. Remove the pan from the oven and cool on a wire rack for 5 minutes. Transfer the individual biscotti to a rack to cool completely. The biscotti will keep in an airtight container for up to 2 weeks.