Beat butter and sugars at medium speed with an electric mixer until light and fluffy. Add peanut butter and next 3 ingredients, beating well.
Combine flour, salt, and baking soda. Add to butter mixture, beating until blended.
Use a cookie gun fitted with a flower-shaped disc to make cookies, following manufacturer's instructions. Place cookies on lightly greased baking sheets. Place a chocolate morsel in the center of each cookie.
Bake at 350° for 8 minutes or until lightly browned. Remove to wire racks to cool. Chill 30 minutes. Freeze up to 1 month, if desired.