Receptacle in a shallow box?

[LarryFine]

Duplex receptacle with GFCI breaker in panel

I would opt for feeding an island from a regular-height wall receptacle; every kitchen should have at least one.

In fact, sometimes I'll put both counter circuits' GFCIs in non-counter outlets, if the buttons would be unsightly.

 

[kwired]

Duplex receptacle with GFCI breaker in panel

In dwellings anymore you likely need AFCI protection as well, so just go with the dual function breaker.