Cut the head of cabbage in half and steam both pieces for 10 minutes each.
Make shallow cuts in the steamed cabbage halves in a grid-like pattern, leaving an uncut rim around the outside edges and bottom of each half. Use a spoon to remove the cut pieces from the center of each piece of cabbage until the halves resemble shallow bowls. Set the pieces you removed from the center aside for later.
Heat a pan with some vegetable oil and fry the minced ginger and garlic. Whisk 2 eggs and pour them into the pan with the garlic and ginger. Add the cooked rice and chopped scallions and sauté everything until the eggs are cooked all the way through. Remove the fried rice from the heat and spoon the mixture into the hollowed-out cabbage bowls.
Cut the pork belly into uniform strips. Heat a large pan on the stove and sauté the pieces of cabbage you set aside earlier, along with the pork belly strips, red miso, soy sauce, sugar, sesame oil, chili powder, minced garlic, and sake, stirring occasionally. Once the pork belly is cooked all the way through, spoon the mixture into the cabbage bowls on top of the fried rice.
Garnish the pork belly fried rice cabbage bowls with chopped scallions and white sesame seeds.