Step 1: Preheat the oven to 350°F (175°C).
Step 2: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Step 3: In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes.
Step 4: Add the peanut butter and mix well. Then add the eggs one at a time, mixing after each addition, followed by the vanilla extract.
Step 5: Gradually add the dry mixture to the wet ingredients, mixing on low until just combined.
Step 6: Fold in the crushed peanuts gently with a spatula.
Step 7: Drop rounded balls of dough onto prepared baking sheets, spacing them 2 inches apart.
Step 8: Bake for 10-12 minutes, until edges are lightly golden.
Step 9: Cool on baking sheets for 5 minutes, then transfer to a cooling rack.
