In cabinets with partial overlay doors, attach the crown molding directly to the face frame. Most partial overlay doors leave you with 1-in. to 1-1/4-in. of the exposed face frame for the molding.
Luckily, with this project, that's not necessary. We're not exaggerating when we say all you need to do is stick the trim to your cabinet door and call it a day. Sure, there may be some clean-up ...