This isn't real tamago. Tamago is egg sushi that is quite sweet. This is just a typical ham-and-cheese omelet wrapped up in a fancy form. Great for brunch. This is my first time trying to make an omelet like this, and I learned a lot about the technique by trying it out.
Ingredients for two omelets
6 eggs, beaten
1-2 slices of thinly sliced or finely diced ham or smoked salmon
1-2 slices thinly sliced cheese (I used Swiss and havarti)
1/2 cup finely diced bell pepper (red, orange, yellow, green, whatever)
2 scallions finely diced
2-4 Tablespoons of olive oil
Salt and pepper to taste
Note: I didn't add milk or water to my eggs. You can try that if you want but I wouldn't dilute it too much as you don't want your egg roll omelet to thin out and tear easily while rolling. I also don't use butter because that will brown the egg, and I don't really like browned omelets. You do it as you like it.
Step 1: Prepare Yourself
Step 2: Pour and Roll and Pour and Roll (and Pour and Roll)
Worried about under-cooking eggs? Don't be.
There is a detail to consider before you start: Do you want your omelet to be yellow or brown? I like my omelets yellow, so my goal is to work quickly and not stall out and not overcook my omelet. There is really no way to undercook this; if it's able to be rolled up, it's cooked enough.
Get ready to repeat yourself
Swab on some olive oil with a brush or a paper towl. Pour in about 1/6th of the egg mixture into the pan. Basically, you're going to coat the pan with a thin layer of egg. If you want to add ham or salmon or whatever, do it in this first roll and make sure that whatever you're adding is thin or diced! Once the egg begins to set, using chopsticks or a rubber spatula (frankly, at times it is best to use both together), begin to roll the edge farthest away from you toward yourself. Do this slowly and try to keep it cylindrical if you can, but it's okay if it becomes more like a brick shape. You want to go slowly because you don't want to tear the omelet.
Once you have rolled up the omelet, push it back to the far edge of the pan. Get the olive oil towl out and apply another thin layer of olive oil. Pour about the same amount of egg mixture you poured last time into the pan. This is important: Your goal is to carefully lift up the omelet so the new egg mixture will pour underneath your rolled omelet and combine with the already cooked omelet. This will ensure that your next roll will be seamless and even. Once the egg begins to set, you're going to continue rolling.
Once you roll up round two, you're going to repeat this again until you feel like you're done. I came to the conclusion that three rounds is about the right amount for me. I tried larger omelets, and I tried a one-egg omelet, which was cute, but 3 seems to make sense. After all, that's the size of a typical 3-egg omelet. Deep down in my soul I feel like doing it with 4 pours using very thinly poured stages of egg mixture would be perfection. Maybe next time.
Step 3: Let Your Omelet Rest
As I say, this was my first time trying this out, and I had a few mis-steps along the way, but I ultimately figured it out and came up with some nice omelets that were different and quite tasty. I'd be very interested to hear if others have ever tried anything like this or if they try it and have any suggestions about how to make it better.