Designing Kitchens and Bathrooms - Installing cabinets under soffit

I am installing new wall cabinets under a soffit. The cabinets I chose are full door, meaning there is no cabinet showing, or edge on the top. The soffit is 14" deep, the cabinets are 12. Can someone advise me on how to hang these so they look good, and the door does not catch on the soffit? I am guessing I need to shim them out to the 14" edge of the soffit, then use molding along the exposed side??

Your cabinets are referred to as a European style and there are several methods that are commonly practice, holding the cabinets out at the front of the soffit is the least of which.
You have some things to consider. Is it your desire to keep the installation as devoid of molding as possible. And if so, have you checked the soffit for irregularities both over its length and "nose" to wall. This can affect the door operation.
If your soffit are not true then I would suggest a narrow crown molding, Hold the cabinet down from the soffit the width of the molding profile, and install a 1x nailer to the top of the cabinets even with the front edge of the box.

I had this same problem when I went to install my 42" tall full overlay (European style) cabinets up to the ceiling, rather than up to a soffit. My run was only at 10' long So I started with the cabinet at one end. Using a countersinking drill bit, I predrilled the cabinet and the molding together at one time while the molding was held in it's correct position. (This was done on the floor). Then I screwed the two together and mounted the end cabinet in place with the crown molding. Since the crown was already cut and mitred to the correct length, I just used it as a filler to keep the cabinet the proper distance from the ceiling. As far as the soffit, do not try to move the cabinets out to 14". That would be difficult to mask and not common. I cannot stress more the idea of laying all the cabinets out ahead of time. This gives you a great way to visualize and forsee any future problems before they happen. With your full overlay cabinet you would want to screw through the "hanging rail" built into the cabinet and make sure the 2.5"--3" screw is attached to a wall stud. Screw the cabinets together in a nice tight fit. Then you should be done.