Preheat oven to 350°F (175°C).
In a large bowl, beat together butter, peanut butter, granulated sugar, and brown sugar until light and fluffy.
Add egg and vanilla extract, mix well.
In another bowl, whisk together flour, baking soda, and salt. Gradually mix into the wet ingredients.
Shape dough into 1-inch balls. Roll each in sugar and place on a parchment-lined baking sheet.
Bake 8–10 minutes until the edges are slightly golden.
Immediately press a chocolate Kiss into the center of each cookie.
Let cool on the sheet for 5 minutes, then transfer to a wire rack.