Preheat the Oven - Set the oven rack to the center position. Preheat to 375°F (191ºC). Line three baking sheets with parchment paper.
Sift the Dry Ingredients - In a medium bowl, sift together flour, baking soda, and salt, then whisk to combine.
Mix the Butter and Sugars - Using a stand mixer fitted with the paddle attachment, cream together butter, peanut butter, granulated sugar, and light brown sugar on medium speed for 1 minute.
Add the Wet Ingredients - Add egg, milk, and vanilla, and mix on medium speed until well blended, about 30 seconds.
Incorporate the Flour - Gradually add the flour mixture, mixing until combined at low speed, about 1 minute. If the dough is very soft, refrigerate for 30 minutes before rolling.
Roll Out the Cookies - Measure 1 leveled tablespoon of cookie dough and roll it into approximately 1"-sized balls. Roll the cookies in sugar and place 2" apart on the baking sheets.
Bake - Bake until lightly browned, puffed, with some cracks on the surface, 8 to 10 minutes. Immediately press the unwrapped chocolate candies into the center of each cookie. The dough will crack more around the edges.
Let Them Cool - Allow the cookies to cool for 2 minutes on the sheet pan, then transfer them to a wire rack.
Notes
Storing: Place cookies in an airtight container for up to 5 days at room temperature. I do not recommend freezing, as the chocolate can bloom, causing the surface to turn white.