In a mixing bowl or stand mixer add together the sugars and butter and cream completely.
Drop in one egg and the peanut butter and cream together again.
Next stir in the salt, baking soda, and vanilla and mix.
Lastly add in the flour and mix until a soft dough forms. It should still be sticky but able to easily form balls without attaching to your hands.
Line the cookie sheet with parchment paper for an easy to clean nonstick surface. Roll the cookies into 1-11/2" balls and space 2 inches apart. Gently press down to slightly flatten each dough ball.
Bake for 6-7 minutes. Remove tray from oven and quickly and gently press in the chocolate kisses into the center but not going all the way to the bottom of the cookie.
Place the cookies back in the oven for 1-2 more minutes to get a firm placement of the kiss melted in. cool on sheet 2 minutes before transferring to a cooling rack.
Optionally drizzle the cookies with icing or caramel once cool. Store in an airtight container in a cool dry place up to 3 days or freeze for up to 3 months.