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. Remove to wire racks to cool. Chill 30 minutes. Freeze up to 1 month, if desired. Makes 8 dozen.