Place 6 large eggs, 1 tablespoon mirin, 1 teaspoon granulated sugar, ½ teaspoon kosher salt, ½ teaspoon hondashi, and ½ teaspoon toasted sesame oil in a medium bowl. Whisk with chopsticks or a fork until no streaks of egg white remain.

Pour the mixture through a fine-mesh strainer into another bowl, swirling the strainer occasionally (this might take a few minutes). Discard the contents of the strainer.

Heat a tamagoyaki pan or medium nonstick pan over medium-low heat. Coat the pan with a thin layer of cooking spray or 1 teaspoon neutral oil. Pour a thin layer of the egg mixture into the pan (about 3 tablespoons), quickly tilting the pan so that the egg mixture covers the entire surface.

Cook until the egg mixture is almost set (about 80%), 3 to 4 minutes. Roll it up, starting at one short end of the tamagoyaki pan furthest away from you, and using chopsticks or two flexible spatulas, roll it down on itself toward you. Slide the rolled omelet to the top of the tamagoyaki pan.

Pour another thin layer of egg mixture into the pan, lifting the already-rolled portion up to let the mixture flow underneath. Repeat cooking and rolling until you use up the egg mixture (5 to 6 batches).

Transfer the omelet seam-side down to a cutting board. Let cool for 5 minutes. Cut crosswise into ½-inch or 1-inch-wide pieces.