I got a cut from an asian grocery store yesterday that was labeled as Pork Belly, but what I got is this:
That's the top-down view; the cut is under an inch thick. There's a portion in the upper right that looks similar to the fat on pork belly.
What would this cut be called, and when I'm cooking it should I look for inspiration in pork chop recipes, or pork belly recipes?
That looks like Pork neck or shoulder without a bone. The best way to prepare it is to grill it or bake.
This looks just like what we buy labeled "pork butt steak". It is a shoulder cut and is very flavorful. It is available both bone-in and boneless. And being the thickness you describe is less than an inch, it certainly sounds like it.
We prepare it many different ways, very similar to how we would prepare pork chops. They are great pan fried, grilled, and breaded and fried.
We actually prefer these to regular pork chop cuts as they are more flavorful and moist.
It's difficult to be sure where that cut came from, although it looks like shoulder. In any case it's clearly fatty and more like belly than like loin, so you would be better served by recipes for belly than chop.
Braising a cut like this is probably your best bet.
Not posting any just because most of the stock photos are copy written, but a quick image search of "raw pork steak" will give you very similar pictures. That one might be cut a bit more of an angle that many to make for easier bone removal. It tends to be fatty as you see, and can have connective tissue and is indeed usually from the shoulder, sometimes closer to the loin. Similar in flavor to chop but can be tougher. Can be grilled, pan seared, braised or is commonly used in many stir fry type dishes cut up. I would tend to recommend is fast cook on high heat or braising. Flavor can be very good, but the connective tissue can be an issue. This is why the shoulder it often the target of sausage.
Many people (I am one) often prefer the flavor to many chops, but fighting the fat and potential connective tissue puts others off. So if cooked more like a chop I would definitely recommend not over cooking with will tend to highlight the potential toughness.
