Lower the eggs into boiling water, cook for 7 minutes, then move them to ice water before peeling and halving.
Bring the broth, ginger, garlic, soy sauce and rice vinegar to a simmer in a wide pot.
Add the mushrooms and simmer until tender, about 5 minutes.
Stir in the pulled pork and cook until it is hot, 3 to 4 minutes.
Add the ramen noodles and simmer just until loosened and tender, about 3 minutes.
Fold in the spinach and remove the pot from the heat as soon as it wilts.
Divide among four bowls and add the halved eggs and scallions.