Bring a large pot of water to a boil and cook the udon noodles according to package instructions until tender.
Drain the noodles and rinse under cold water to prevent sticking, then set aside.
In a medium pot, combine the dashi stock, tamari, mirin, and grated fresh ginger, bringing the mixture to a gentle simmer over medium heat.
Add the baby bok choy and shrimp to the broth, poaching for about 3 minutes until the shrimp are pink and the greens are wilted.
Prepare the egg by soft-boiling it in a separate small pot of boiling water for 6 minutes, then cooling in an ice bath and peeling.
Place the cooked noodles into a large serving bowl and ladle the hot broth, shrimp, and bok choy over the top.
Slice the soft-boiled egg in half and place it on the noodles, then finish with a garnish of sliced scallions, sea salt, and black pepper.