One way is to just run your outside corner as usual with 45* miter cuts on either side and fill in the gap. I prefer this way. For filling large gaps like this I prefer using automotive filler (bondo) or the two part minwax high performance filler which is really the same stuff for double the price. Before it is completely dry shave it smooth with a razor or wipe smooth with a rag and acetone. Don't leave any high spots b/c this stuff is murder to sand. Finish off with some vinyl spackle and you are done.
Another way is to cut 22.5* miters and use an extra piece in the miter. This would be a small piece between the two main wall pieces and would sort of bend the moulding around the corner. All cuts are 22.5* and you still will have some filling to do.