Hambaagu (or "hamburg", as in "hamburger" without the "-er") is something I grew up with, and wondered why we didn't eat them inside a bread bun like other people. (...And why my mother called them "hambaagu", without the "-er" or "patty"!) I've figured out the answer since then: Hambaagu is a Japanese thing.
The special thing about these hamburg, is that they're still soft, even after they cool down - one of the requirements for delicious obento foods. The secret is: lots of panko breadcrumbs, and after cooking on both sides, add a little water to the frypan, put the lid on and steam them, similar to making Japanese-style pan-fried gyouza. The panko absorbs the water and holds the moisture in.
I learnt how to make these watching a cooking show on Japanese TV, teaching mothers how to make obento for their kids when they start kindergarten. Mini-Hamburg and Chicken Karaage were named as the favorite bento "main" okazu for kids. (Japanese cooking shows are really useful!) I didn't write down the recipe at the time so I pretty much guessed it. You can't go wrong. I cook mine on a large electric okonomiyaki hotplate.
400g pork mince (if your mince is low fat, mix in 1 Tbsp vegetable oil or Japanese mayonnaise)
Panko or homemade breadcrumbs: Almost the same volume as mince (maybe 1 cup? didn't measure)
1 small onion, sliced very finely
1 Tbsp milk
1 Tbsp soy sauce
2 tsp sugar
a sprinkle of salt and pepper
1. Combine all ingredients in a bowl. It should be moist, if not, add another Tbsp milk.
2. Pre-heat a large frypan to med heat, wipe with a little oil.
3. Shape mini-hamburg in your hand and place them on the frypan (about 4~5cm dia)
4. Turn when browned and cook until browned on both sides.
5. Pour a little water onto the frypan (enough to cover the base of the frypan, about 1/4 cup, depending on the size of the frypan and how much you are cooking) and immediately put the lid on to keep the steam in. After a few minutes when all the water has absorbed into the hamburg, they're done! (Be careful not to burn yourself with steam when you open the lid.)6. Wash the residue from the frypan before cooking the next batch.
1. Allow to cool before bagging for the freezer.
2. Laying the bagged hamburg out on a baking tray allows them to freeze faster and keeps them separate.
3. Once they're frozen, place all the bags into a freezer-safe lidded container, and they'll be fresh for up to a month. (I use one with a hinged lid, it's easier to open and close)
4. Reheat 3 hamburg on a plate in the microwave on high for 1 minute, or until they are hot right though. Use however you like in your bento.