Dump in half of the scallions, the ground pork, soy sauce, salt, and pepper, and cook, breaking up the meat with a wooden spoon until the pork is cooked through, about 5 minutes. Pour in the beef stock and bring to a boil.
Add the oil to a large saucepan over medium heat. Toss in the ginger and cook until fragrant and slightly softened, 1 to 2 minutes, stirring frequently. Add the garlic and cook an additional minute. (Don't let it brown or it will become bitter.)
Poach the eggs: Fill a medium saucepan two-thirds full with water (at least 3 inches deep) and bring to a gentle simmer. Very gently crack the eggs, working one at a time, into the simmering water, keeping the whites and yolks as intact as possible. Cook until the whites have firmed up and no longer look runny, 3 to 4 minutes. Using a slotted spoon, transfer the eggs to a bowl, lift the eggs out, let excess water drip back into pan, and set aside. While the eggs cook, fill a third pot with enough water to cook the noodles; bring to a oil. Add the noodles and cook until al dente, about 6 minutes; drain.
Divide the noodles, meat, and eggs between two serving bowls. Ladle in the broth. Top with the remaining scallions.