Hand Tools Archive
I used the type of hinge you're talking about on my kitchen cabinets, and then before that, amerock hinges in HUGE amounts working at Aristokraft in college (similar style, no soft close for us at the time).
I don't remember seeing anything that was made for doors that are partially recessed, and as you mention, I could suggest a cobble.
But, I would first call Blum and ask them if they have anything for the application.
I'd imagine that long ago, they went away from what I'm used to and toward cabinet mount hinges for frameless cabinets (much cheaper to make), but partial recess and partial overlay doors are probably even less common than face frame - and if they have a solution, it just may not show up.
I had doors of that type on my last cabinet, but the hinge types were simple where the hinges itself attached to the back side of the door lip and part was exposed right on the face frame.