Bathroom outlet in side of cabinet and inside cabinet? HOW?

Would there be anything wrong with the following in a bathroom remodel?


The bathroom sink cabinet has an open back but it also has a permanent "shelf" where the top of the doors and bottom of the false fronts are. In other words, the area under the countertop and to the left and right of the sink are completely inaccessible. No moving parts, etc.

I do not want to put an outlet in the tile behind the sink cabinet and was hoping to put it in the side of the cabinet instead. Can I run the 12/2 romex directly out of the wall, into the inaccessible space to the right of the sink, and terminate in a box/gfci outlet that is flush on the side of the cabinet? Does the romex need to be protected in this little cubbie?

Say two base cabinets have a 3" filler between the two. Could you simply run the romex in that void, to the box cut in the face of the 3" filler? Or would it have to be protected? If protected, how would one go from romex to shielded?

If I have one outlet inside the cabinet (actually just in the wall itself but cabinet is open-back design) and one outlet on the side of the cabinet, can I make the inside one GFCI for aesthetics or does the MOST accessible outlet have to be the GFCI one? They put GFCI under kitchen sinks so I would assume this is legal?

Thanks in advance! #Lighting&Electrical
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