In a medium bowl, whisk together flour, salt and baking soda. In a large bowl using either a hand or stand mixer, beat softened butter with peanut butter and both sugars until light and fluffy.
Add in egg and vanilla extract, beat until smooth. Add the flour mixture in two additions, beating after each until fully incorporated. Cover and refrigerate dough for at least one hour.
Preheat oven to 350 F. Roll cookie dough into balls and place 2-inches apart onto ungreased baking sheets. Bake for 10-12 minutes. Remove from oven and place one chocolate kiss in the center of each cookie. Let cool.
