I've seen a few sort of like this and wasn't sure what to call them. This one's the most exteme example of the look I'm talking about, so if anyone can tell me what this is (or if it's just "crater"), I'd appreciate it. By the way, I see a face at a 45 degree angle. With an eye patch. I hereby name this crater "Whitebeard The Pirate".

ID: AMZ10033rq
Latitude: -3.20881°
Longitude: 336.639°
Sun Angle: -88.67°
Scale: 0.49 meters / pixel
Hi DJ_59,
I mentioned this somewhere else, but I forgot where.... So, I will have to write it out again

And, I'll add some reference links for good measure.
These types of craters are believed to form when there is a weaker layer overlying a stronger layer (like regolith over a mare layer). For small craters, the strength of the target material is important, so the 2 layers effectively produce 2 craters. A larger crater forms in the weaker regolith, and a smaller crater, nested inside the bigger one, forms in the stronger mare, giving you something that's called a concentric crater.
The original papers that did experiments on this are available by subscription only, so here's a link to a publicly available paper that did the same thing in computer simulations.
Senft & Stewart, JGR 2007. Scroll down to page 14 for pictures of the various types of craters and how they relate to the thickness of the overlying regolith layer.
Now, the crater here is also asymmetrical. That suggests that it was an oblique impact, with the impactor coming from the left.
I hope this helps.