This is probably my favourite dish of all time. It's not even so much a dish as much as a preparation. "Onsen" means "hot spring" in Japanese and "tamago" means "egg.
Since Japan sits on top of a giant volcano, there are hot springs all over the place. Some of these hot springs happen to be be exactly 160 degrees F which is the perfect temperature to slow cook eggs. For those that have never had one, it's one of those experiences where you take a bite and exclaim "I had no idea eggs could taste like this!"
The white has the texture of a really delicate custard while the yolk comes out firm, but retains the color and creamy texture of an uncooked yolk. The traditional way to eat them is for breakfast covered in seasoned bonito dashi, but I love these so much I put them in just about anything. In noodle soups, donburi's, butternut squash soup, or on fried rice. I've even contemplated turning it into a dessert with a sweet caramel syrup (a deconstructed creme caramel)
I won't lie to you, they are tricky to get right, but with the right equipment and a couple of try's you should be able to get it just right. The difficult part is in keeping the temperature just right. All you need is an instant read thermometer, a heavy pot with a lid (like a Le Crueset), and a timer. If you're lucky enough to have an oven that can accurately maintain a temp of 170 degrees it's even easier.
One last note, the FDA recommends you cook poultry products to 165 degrees F. Since we're not quite hitting that, the FDA would consider it "unsafe", but I've never gotten sick eating these and I've been told that prolonged temperatures above 140 degrees F kills salmonella. Still if you're nervous about this kind of stuff this might not be for you.
6 free range eggs at room temperature (you may want to make less the first time)
small enameled cast iron pot with lid (like a Le Creuset)
Take the eggs out of the fridge about an hour before you make this so they have a chance to come to room temperature (this is important). Preheat your oven to 170 degrees F (or as low as it will go)
Fill the pot with water and heat over the stove until your thermometer reads 155 degrees F. Gently lower the whole eggs into the water, cover with the lid and place the whole thing in the oven.
This is where it gets a little tricky. You want to slowly raise the temperature of the water from 155 degrees F to 160 degrees. Any cooler and the egg won't cook, any hotter and you'll have a soft boiled egg (not the same as a slow cooked egg). For my oven, this means setting it to 170, and putting the pot in for 45 minutes. If your oven doesn't go down to 170, you'll need to check the temperature of the water periodically and turn off the oven, then turn it back on to try to keep the temperature under 160.
It may sound like a ton of work, but it's worth it, and once you make a batch you can keep them in the fridge for up to a week and use them as you need them.
Unfortunately there's no way to tell if they are done without cracking them open, so you'll need to rely on your thermometer and timer. To serve, just crack it open into a small bowl and cover with a splash of salted dashi. Good luck!