Heat oven to 350 degrees F. Line 2 large cookie sheets with parchment paper or silicone mats.
Sift together flour, soda and salt and set aside.
In a stand mixer with the paddle attachment (or by hand), beat together softened butter and peanut butter until light and fluffy.
Gradually add sugars and beat until well blended.
Beat in egg and vanilla until well blended.
Stir in flour mixture just until incorporated. Form into 1-inch balls using about a tablespoon of dough for each. Roll in granulated sugar and place on ungreased cookie sheets. Bake at 350° for 8 minutes then remove from the oven and gently place a chocolate kiss on top of each cookie until it cracks around the edges.
Bake 2-3 minutes more until golden.
Cool for several minutes on the baking sheet before transferring to a rack to cool completely.
Store cooled cookies in an air-tight container for up to 3 days for maximum flavor and texture. Freeze in an airtight container for up to 6 months.
When putting the cookie back into the oven with the kisses on top, watch closely. Do not let the chocolate burn, but you want it to get almost to that point. 2-3 minutes is usually perfect, but can vary by oven.