Preheat the oven to 350°F and line a baking sheet with parchment paper and set aside.
In a large bowl, whisk together the flour, baking soda, baking powder, and salt and set aside.
In a large bowl or stand mixer fitted with a paddle attachment, cream together the butter, peanut butter, light brown sugar, and ½ cup of granulated sugar until light and fluffy.
Scrape down the sides and bottom of the bowl and beat in the egg and vanilla until well combined.
Add in the dry ingredients and mix just until incorporated.
Use a medium cookie scoop to portion out the dough and roll into balls. Roll the dough in the remaining ½ cup of granulated sugar and place the balls on the prepared baking sheet about 2-inches apart and bake for 8 minutes.
Remove from the oven and press the candy into the center of the cookie and bake for an additional 2 minutes.
Remove from the oven and allow the cookies to cool on the pan for a few minutes before transferring to a wire rack to cool completely.