These cookies are supposed to be thin and crispy. I've made them for several years and have learned a thing or two, so take a look at the notes if you get a chance.
The original version says to bake at 350 F, but I've found I get a more evenly baked cookies when I bake at 325F for slightly longer. I also get nicely shaped cookies when I scoop all the dough ahead of time into balls, press the balls into little discs, chill the discs for several hours, then bake. When baking chilled, preformed dough, the cookies sometimes take up to 20 minutes. Check at 12 and then keep an eye on them.