Preheat the oven to 350 F. Line baking sheets with parchment paper.
Combine the flour, baking powder, and salt; whisk to blend and set aside.
In a mixing bowl with an electric mixer, beat the peanut butter with the butter until smooth and creamy; add the brown and granulated sugars and beat until fluffy, about 3 minutes.
Add the eggs and vanilla and beat until well blended.
With the mixer on low, add the flour mixture and beat just until combined.
Fold in the chocolate chips and peanuts, if using.
Use a cookie scoop to drop the dough onto the prepared baking sheets. Sprinkle with sugar,
or press each mound lightly with a flat bottom glass that has been dipped in the sugar.
Bake until the edges are set, and the tops are soft, about 16 to 19 minutes.
If baking on more than one rack, rotate the pans from top to bottom to ensure even baking.