Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.
In a large mixing bowl, combine the creamy peanut butter, granulated sugar, brown sugar, vanilla extract, and egg. Use an electric mixer or whisk to blend the mixture until smooth and creamy.
In a separate bowl, mix together the baking soda, salt, and all-purpose flour.
Gradually add the flour mixture to the peanut butter mixture, stirring until well combined.
Using your hands, form small balls of dough (about 1 inch in diameter) and place them on the prepared baking sheet, spaced about 2 inches apart.
Bake in the preheated oven for 8-10 minutes, or until the edges are lightly golden. The center will look soft.
Remove from the oven and immediately press a chocolate kiss into the center of each cookie. Allow the cookies to cool on the baking sheet for about 5 minutes, then transfer them to a wire rack to cool completely.