Preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened butter, peanut butter, granulated sugar, and light brown sugar together until creamy and smooth, about 2 minutes.
Add the egg and vanilla extract to the butter mixture and beat until fully combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Place the granulated sugar for rolling in a small bowl.
Using a tablespoon or cookie scoop, scoop dough and roll into 1-inch balls. Roll each ball in the granulated sugar to coat lightly.
Place the sugar-coated dough balls on the prepared baking sheets about 2 inches apart.
Bake in the preheated oven for 8 to 10 minutes, or until the edges are set but the centers are still soft.
Remove the cookies from the oven and immediately press one chocolate kiss into the center of each cookie, gently pressing down to slightly flatten the cookie around the chocolate.
Allow the cookies to cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely.