Preheat your oven to 375°F (190°C). Prepare a baking sheet by lining it with parchment paper or a silicone baking mat to prevent the cookies from sticking.
In a large bowl, use an electric mixer or a stand mix to cream together the butter and the peanut butter until light and fluffy, about 3 minutes.
Add in the white granulated sugar and light brown sugar to the peanut butter mixture. Continue mixing until the sugars are thoroughly incorporated and the mixture is light and fluffy.
Crack the egg into the mixture, add the vanilla extract, and mix until the egg is fully incorporated.
Add the flour and baking soda to the wet ingredients. Stir until just combined. Do not overmix.
Using a cookie scoop or a tablespoon, scoop out portions of dough. Roll each portion between your hands to form a smooth ball.
Bake the cookies in your preheated oven for 8-10 minutes, or until the edges are lightly browned but the center is still soft.
Gently press an unwrapped Hershey kiss into the center of each warm cookie. Be careful not to push too hard or the cookie may crack. I like to let the cookies cool a few minutes before adding the kisses to they don't melt too much.
Allow the cookies to cool on the baking sheet for 5-10 minutes, then transfer them to a wire rack to cool completely.
Notes
Using room temperature butter and egg will help your ingredients mix together more uniformly, creating a better texture in your cookies.
Overbaking can cause your cookies to become hard. The cookies will continue to cook slightly on the hot baking sheet even after you remove them from the oven, so it's better to err on the side of underbaking.
To store these cookies, keep them in an airtight container at room temperature. They should stay fresh for up to a week.
If you prefer a different type of Hershey's kiss, feel free to substitute. Just keep in mind that different types may melt at different rates and have different flavors.