Preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large bowl, beat the softened unsalted butter, granulated sugar, and light brown sugar together until creamy and smooth, about 2 minutes.
Add the creamy peanut butter to the butter and sugar mixture and beat until combined.
Add the egg, vanilla extract, and milk to the mixture and beat until fully incorporated.
Gradually add the dry flour mixture to the wet ingredients, mixing until just combined.
Roll the dough into 1-inch balls and place them about 2 inches apart on the prepared baking sheets.
Bake the cookies in the preheated oven for 8 to 10 minutes, or until the edges are lightly golden but the centers are still soft.
Immediately after removing the cookies from the oven, press one unwrapped chocolate kiss into the center of each cookie. The cookie will crack slightly around the edges, which is normal.
Allow the cookies to cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.