Preheat the oven to 350F. Line two baking sheets with parchment paper and set them aside.
In a large bowl with an electric mixer on medium speed, beat the butter, brown sugar, and a 1/2 cup granulated sugar until light and fluffy.
Add the peanut butter, egg, and vanilla extract to the sugar mixture. Beat on medium speed until fluffy, about 2 minutes.
Add the flour, baking soda, and salt to the peanut butter mixture and mix on low speed until just combined.
Form the dough into 1.5-inch balls (about 3 tablespoons) and roll them in the remaining 1/4 cup of granulated sugar. Place the dough balls on the two baking sheets approx 1.5 inches apart.
Place the unwrapped chocolate kisses in the freezer while the cookies bake. Bake the cookies for 10-15 min until the edges are just set and the center is no longer liquid. You don’t want the whole cookie to be firm because they firm up more as they cool.
Right after removing the cookies from the oven, push the slightly frozen chocolate kisses into the center of each cookie. Let the cookies cool on the pan for about 5 minutes or until you can move them without them breaking. Transfer the cookies to a wire rack to continue cooling. As the cookies cool, the chocolate kisses will melt a little and keep their shape. These are best served when they are still warm, but they will stay fresh for 3 to 4 days when stored at room temperature in an airtight container.