In a small bowl, whisk together the flour, baking soda, and salt.
In a mixing bowl, beat the butter, peanut butter, sugar, and brown sugar until fluffy, scraping down as needed, for about 7 minutes.
Add the flour mixture to the creamed sugars and beat until mixed, scraping down as needed.
Cover the cookie dough and refrigerate for 1 hour.
When ready to bake: Preheat the oven to 325 degrees. Prepare a mini-muffin baking sheet with nonstick cooking spray.
Using a small cookie scoop, portion the cookie dough and place in the prepared mini-muffin pan.
Bake the cookies for 14 minutes and then move to rest on a wire rack. The middles of the cookies will fall slightly.
For the fudge: In a large microwave-safe bowl, place the milk chocolate chips, the semi-sweet chocolate chips, and the milk. Heat for 1 minute on high and stir vigorously to allow the chocolate to continue melting from the residual heat. Repeat in 30 second increments if needed, taking care to not overheat the chocolate. When the chocolate is melted and smooth, stir in the vanilla.
Transfer the fudge filling into a piping bag with the corner snipped or use two spoons to place a small dollop of fudge into the well of each cookie.
After the fudge has cooled slightly, you can use a piece of waxed paper or a damp finger to smooth the tops of the fudge centers.
Using a spoon, lift the cookie cups from the mini-muffin pan and allow to cool completely prior to storing in an airtight container.