Mix flour, baking soda, and salt together in a medium-sized bowl. Set aside.
Cream together the shortening/butter, peanut butter, white sugar and brown sugar. Add egg, milk, and vanilla. Beat well.
Gradually add dry ingredients to wet ones, and beat until smooth.
Shape into golf-ball-sized balls. Roll in white sugar.
Bake at 375 degrees on a lightly greased cookie sheet for 8 minutes. If they seem to be cooking too fast (getting too dark) try lowering your oven temperature to 350 degrees.
Remove from oven. Press a chocolate star firmly into each cookie. Return to oven and bake 4 minutes more.
I let mine cool on the cookie sheet for about 5 minutes before removing to wire racks to cool. This made about 45-50 cookies. The amount of cookies it makes depends on the size of your dough balls (smaller ones make more).