When I worked as a delivery driver for a take-out Sushi place some years back, I saw how they made the tamago brick that was created before it was sliced. They used a special rectangular egg pan that they would pour the beaten mix in, let it set, then fold it on top of itself, add more mixture, and continue the process until a brick was completed, then refrigerated until it was sliced for the sushi order. A few bricks were made daily, and usually as sold out before the end of the day.