Beat the butter, 1 cup granulated sugar, and light brown sugar until light and fluffy. Add 1 1/2 cups of peanut butter, eggs, and vanilla extract; mix until smooth.

In a separate bowl, whisk together flour, baking powder, baking soda, and salt. Gradually blend the dry ingredients into the wet mixture until just combined.

Cover the bowl with plastic wrap and refrigerate the dough for 30 minutes. This helps prevent the cookies from spreading too much.

Scoop the dough into about 24 balls and flatten them in your hand. With each, make a small well in the center and add about 1 teaspoon of the reserved peanut butter. Gently fold the dough over the filling and roll into a smooth ball. Roll each ball in the extra 1/2 cup granulated sugar.

Place the cookie balls 2 inches apart on a parchment-lined baking sheet. Bake at 350°F for 13 minutes or until the edges turn a light golden brown. Allow the cookies to cool on the sheet for a few minutes before transferring to a wire rack to cool completely.