Peel the onions then cut in half lengthwise and slice. To make the Katsudon sauce, combine the dashi stock, mirin, sugar, and soy sauce. Set aside.
Break the eggs in a separate bowl and lightly beat them. You want part of the yolk and whites to be lightly mixed, while other parts are separated. Set aside.
Prepare the Katsudon one serving at a time. In a small skillet (a 6-inch or 7-inch skillet works great), spread half of the onions and pour half of the Katsudon sauce. Bring to a boil over medium heat for about 5 minutes, or until the onions soften. Place a sliced tonkatsu fillet in the sauce and cook for another 30 seconds. Pour one-half of the egg mixture over the tonkatsu, onions, and sauce. Do not mix. Cover the skillet and cook for another 30 seconds. Remove the skillet from heat and let the Katsudon rest, covered, for about 1 minute.
While the Katsudon is resting, scoop a cup of cooked white rice in a shallow bowl. When the Katsudon is ready, uncover the skillet and slide entire contents onto the rice. Tilt the skillet and use a spatula if necessary. Garnish with sliced green onions and a sprinkle of Togarashi. Repeat the same steps for the remaining serving.
(Note 1) Dashi is a Japanese stock, and it is a fundamental ingredient in many Japanese dishes. It is used in many Japanese dishes, such as miso soup and donburi. Without dashi in Japanese cooking, it lacks authenticity. Nowadays there are MSG-free Dashi granules/powders available at Japanese grocery stores, but it is quite difficult to find in Asian grocery stores. I use dashi granules and dissolve them in water, just like how you would use a normal chicken/beef powder or cubes to make a stock.(Note 2) To make Tonkatsu, lay the pork fillets (use boneless pork shoulder or pork loin) on a cutting board. Pound each side to flatten the meat to about 1/2 inch thick. Cut 1/2-inch notches into the white fat of the pork (if there is) to prevent the meat from curling when frying. Season the fillets with salt and pepper. Bread the pork fillets by dipping them in this order: flour, beaten egg, and panko before deep frying them in oil that has heated to 340F.