How to install crown molding or valance board around a cabinet?
If the gap bothers you that much, you have a few options.
Fill the gap
You could fill the gap with wood putty, or color matched caulk. You'll still have a gap, but it will be difficult to see.
Remove material from the molding
You could remove a bit of the material from the back of the molding, to allow it to lay flat over the lip of the cabinet. This will likely make the mitered joint between the two pieces of molding look odd, as the bottom of the pieces will not mate.
Remove material from the cabinet
You could remove a bit of the material from the cabinet, to allow the molding to lay flush with the side of the cabinet. Depending on how far out the cabinet overhangs, this might also look a bit strange.
Learn to live with it
The easiest approach, is to simply learn to ignore it. Not many folks will notice it, and after some time you probably won't either.