It's called Aussie Burger and is located in Kyung Sung a few doors down from OL '55 going towards the back fence of Pukyong university (see below map), a good location, but at the same time you might not know where it is unless you happened to be walking past it.
The owner lived in Australia for several years which seems to have served him well. Unlike a lot of other burgers in town they are big and wide rather than narrow and high (which I can never fit in my mouth!). He also only has one basic burger on his menu - cost 5,800 won which has the burger, cheese and red onion with sauce on the side. To that you can add whatever you want. Bacon at a buck, lettuce and tomato at 20 cents and 50 cents respectively, an extra patty for 2 bucks and a host of other things including egg, pineapple and cheese. Or you can go for 'The Lot' at a very reasonable 8,700 won.
Other items on the menu other than burgers include.
Meat Pies!! Yep, good 'ol Aussie meat pies. Perhaps a little too much butter in the pastry, but regardless it's great to have a pie again. 5 bucks
Potato wedges (seasoned really well with a touch of heat added from I think cumin), served with chilli sauce, thai sweet chilli sauce and sour cream. For just a buck and a half.
Clam Chowder - 2 bucks
As well as cheesy fries, homemade cheese sticks, cheese on toast and salad.
He also has Cafri on tap, plus free soda refills.
Out of a table of six the overwhelming consensus was that not only was it one of the best burgers they've had in Korea, a few went as far to say that it was the best burger they've had in Busan. And that's from a guy that has tried all of the burger options here in Busan and is one of the harshest critics I know!
The decor and design of the place is also very good. Modern, but comfortable. They also have outdoor seating, which I think will be very popular come the summer. The staff were friendly, with decent English and the owner himself was very nice and helpful.
I've also been told that they will take out orders if you wanted to eat at home or outside Family Mart!