Place 1¾ cup all-purpose flour, 1 teaspoon baking soda, and ½ teaspoon salt in a medium bowl, and whisk to combine.
Place ½ cup butter, ½ cup peanut butter, ½ cup brown sugar, and ½ cup granulated sugar in a large bowl. Mix on medium speed with a hand mixer or stand mixer until light and fluffy.
Add 1 egg and 1 teaspoon vanilla extract, and stir to combine. Stir in 2 tablespoons milk.
Add the flour mixture and stir just until combined.
Roll into 1¼ inch balls and roll in additional granulated sugar. Place the balls at least two inches apart on a baking sheet. Bake for 10 minutes.
When the cookies get out of the oven, press a chocolate star in the center of each one.
Let cool completely on a wire rack, and enjoy!
Notes
I found the chocolate stars at Farm and Fleet. If you can't find them at your local grocery store, try an internet search for "chocolate star candy" to see if there are any other sources near you. If not, try one of these other ideas: