The recipe that I used calls for baking powder and baking soda, so the dough rises a bit. Any recommendations as to the sort of cookie dough that would retain an imprint?
Speculoos or Dutch windmill cookies.
Use a sugar cookie dough that doesn't have any baking powder or soda in it. After you cut them out, refrigerate for about 10 minutes before baking.
Shortbreads are usually quite oven stable.