Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, beat together the softened butter, peanut butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes. Add the egg, milk, and vanilla extract. Mix until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry ingredients to the wet mixture, mixing on low speed until just incorporated.
Scoop out about 1 tablespoon of dough and roll it into a ball. Roll each ball in additional granulated sugar to coat evenly.
Place the dough balls onto the prepared baking sheets, spacing them about 2 inches (5 cm) apart.
Bake in the preheated oven for 8-10 minutes, or until the edges are lightly golden and the tops are slightly cracked.
While the cookies are baking, ensure all chocolate kisses are unwrapped.
Immediately upon removing the cookies from the oven, press a chocolate kiss into the center of each cookie. The cookies may crack slightly around the edges when the chocolate is pressed in; this is normal.
Allow the cookies to cool on the baking sheet for 5 minutes. Transfer them to a wire rack to cool completely. The chocolate will soften from the heat but will firm up again as the cookies cool.