Preheat the oven to 375°F. Lightly grease a 24-cup mini muffin pan with nonstick cooking spray.
In a medium bowl, whisk together the flour, salt, and baking soda. Set aside.
In a large mixing bowl, beat the softened butter, granulated sugar, peanut butter, and brown sugar until light and fluffy.
Add the beaten egg, vanilla extract, and milk. Beat until well combined.
Gradually add the dry ingredients to the peanut butter mixture. Mix just until the dough comes together; do not overmix.
Roll the dough into 1-inch balls. Place one ball into each mini muffin cup.
Bake for about 8 minutes, just until the cookie dough is set around the edges. Do not overbake.
Immediately after removing the pan from the oven, gently press one unwrapped mini Reese's peanut butter cup into the center of each cookie.
Allow the cookies to cool completely in the pan before carefully removing them. A small butter knife can be used to loosen the edges if needed.