Heat the olive oil in a large pan over medium heat. Add the onions and garlic and saute until the onions are golden, then set aside to cool.

Mix the water, sesame oil, and panko in a large bowl. You're going to add all the other ingredients to this bowl, so make sure to use something big enough.

Combine all the remaining patty ingredients (not the ponzu or the vegetable oil) and mix thoroughly.

Divide the meat into 6 or 8 portions, depending on how many people you're feeding and how big you want the patties to be. Cover your hands with a little olive oil to prevent the mixture from sticking to you. Form each portion of hambagu mixture into a tight ball in your hands. Roll the ball and toss it back and forth in your hands for 30 seconds or so in order to force air out of the mixture. Squash each ball into a patty, but be sure not to make it as flat as a Western-style burger. Use your thumb to make an indentation in each of the patties. The burger should be fairly thick throughout. Set the formed patties aside on a plate and cover with plastic wrap. Set the patties aside for 30 minutes (if it's warm in your kitchen you should refrigerate the meat, but make sure to bring it back to room temperature before cooking).

While the patties are sitting, prepare ponzu (if making one from scratch) and condiments.

Heat the vegetable oil in a very large frying pan (I like to use cast iron, but nonstick will work too) over medium heat. Add the patties to the pan, taking care not to crowd them together. Brown the patties for about 4 minutes - don't move them until they're ready to flip.

Flip the patties over and cover the pan to to cook the other side. Let them cook for about 5 minutes, at which point the patties should be cooked most of the way through.

Remove the lid and increase the heat to medium-high. Pour the ponzu over the hamburgers and continue to cook for an additional 2 minutes, spooning the sauce over the patties during this time. Remove the burgers from the pan and place them on a plate to rest.

(Optional) Increase the heat in the pan to high and cook the remaining sauce until it's reduced by one-third to one-half. Serve the reduced sauce over the burgers or on the side. If you find the sauce too salty, add a tablespoon of mirin.

To make grated daikon (daikon oroshi), ideally you'll want to have an oroshigane (Japanese fine-toothed grater). Simply cut and peel a small section of daikon, then rub the cut face in circles over the oroshigane to make a fine puree. Place the grated daikon in a small piece of cheesecloth and squeeze out the excess moisture. If you don't have an oroshigane, use the finest grater that you can find and follow the same steps.

To make the Japanese mustard/mayo, simply mix the mayonnaise and the karashi mustard powder together in a small bowl and serve on the side or over the burger. Be warned, the mustard tends to pack a spicy punch.