In a medium bowl, whisk together the all-purpose flour, baking soda and salt. Set aside.

In a large bowl, using a hand mixer or a stand mixer fitted with a paddle attachment, beat the butter on high speed for 1 minute until creamy. Switch to medium-high speed and add the brown sugar and ¼ cup of granulated sugar. Beat until the mixture is completely creamed and smooth, about 2 minutes.

Add the egg to the mixture and beat until well combined. Scrape down the sides and bottom of the bowl as needed.

Next, add the peanut butter and vanilla extract. Beat until everything is well combined.

On low-speed, gradually add the flour mixture to the wet ingredients and beat until fully combined. The dough will have a creamy and soft consistency. Cover the bowl and chill the cookie dough in the refrigerator for at least 1 hour.

Preheat oven to 350°F and line two large baking sheets with parchment paper or silicone baking mats.

Using a 1-tablespoon cookie scoop, scoop dough and roll it into a ball. Roll each ball in the remaining ½ cup of sugar and arrange on the prepared baking sheets.

Bake the cookies for 11–13 minutes, until golden brown and the tops begin to slightly crack. Remove the cookies from the oven and let them cool on the baking sheets for 5 minutes.

Press a chocolate star candy into the center of each cookie and allow cookies to cool completely.