Mix the flour, soda, and salt in the small bowl. Set aside.
Using the stand mixer, blend the butter and peanut butter. Beat in sugars until well blended. Beat in eggs and vanilla. Gradually add dry ingredients. Add two or three more tablespoons of flour if the dough is sticky. Dough should feel firm to the touch.
Roll dough into 1-inch balls, and roll each in sugar. Bake on ungreased cookie sheet for 10 to 12 minutes or until golden.
Press a chocolate kiss into each cookie while it’s still hot and allow to sit for about 5 minutes on the cookie sheet. Move cookies onto wire rack to cool. The chocolate kisses will remain soft for a while, so wait until the chocolate firms up before moving cookies into plastic storage containers. Makes about 4 dozen cookies.