Heat oven to 400°F. Season pork with salt and pepper. Heat neutral oil in an ovenproof skillet; brown pork on all sides, 5–6 minutes.
Roast 12–18 minutes until pork reaches 145°F. Rest at least 3 minutes; slice thinly.
Simmer eggs in a separate pot 9 minutes; chill in ice water, peel and halve.
Heat sesame oil in a soup pot. Cook garlic and ginger 30 seconds. Add broth and soy sauce; simmer. Add bok choy; cook 3–4 minutes until tender.
Cook noodles separately according to package directions; drain. Whisk miso with 1/2 cup hot broth, then stir into soup off heat.
Divide noodles and broth among bowls. Add pork, eggs and scallions.