1. Cook sushi rice according to package instructions and set aside.
2. Chop the baby bok choy, carrots, brussels sprouts, and butternut squash into bite-sized pieces.
3. In a large pan, heat a tablespoon of butter and sauté the vegetables until tender.
4. In another pan, heat a tablespoon of mirin, sake, and soy sauce. Add the chashu pork, and cook for a few minutes until heated through.
5. In a separate pot, bring the pork broth to a boil. Add the bamboo shoots and simmer until they are tender.
6. In a small pan, fry an egg for each serving of the dish.
7. Assemble the rice bowls by placing a generous portion of sushi rice in each bowl. Top with the sautéed vegetables, chashu pork, bamboo shoots, and a fried egg. Drizzle the dish with the remaining mirin, sake, and soy sauce mixture.
8. Garnish with a sprinkle of basil before serving.