Preheat oven to 375 degrees F. Grease two baking sheets or line with parchment or silicone mats.
In a large bowl, use an electric mixer to cream together granulated sugar, brown sugar and butter. Add egg, peanut butter and vanilla extract. Beat well.
In a separate bowl, whisk (or sift) together flour, salt and baking soda. Gradually add the dry ingredients to the butter mixture; mix just until combined. Optional, but recommended: cover and chill dough for up to 30 minutes for really thick, chewy cookies.
Place about ½ cup of additional granulated sugar in a shallow bowl. Using a cookie scoop (about 1 ½ tablespoons), roll dough into balls and coat in sugar. Place about 2 inches apart on greased baking sheets.
Bake in the 375 degree F oven for 9-10 minutes, or until the tops begin to crack a little bit. The cookies will still be soft. Remove the baking sheets from the oven and place on wire racks to cool. Let the cookies cool for 2-3 minutes, then place a chocolate kiss in the center of each cookie, pressing down slightly. Cool on the baking sheets for about 3-5 more minutes, and then transfer to wire racks to cool completely.