Fill a pot with enough water to cover the eggs, and bring to a boil. Gently lower the eggs into the boiling water using a slotted spoon (simmer for 5 minutes for a runny yolk or 8 minutes for a harder yolk). Add the ramen noodles to the boiling water with the eggs and cook according to the instructions on the package. Drain well and set aside. Meanwhile, fill a large bowl with ice water. When the timer finishes on the eggs, transfer the eggs to the ice bath using a slotted spoon to stop the cooking process. Wait at least 5 minutes, or until cool enough to handle, then carefully peel away the shell. Set aside until ready to serve.
Season the steak generously with salt and pepper. heat half of the oil in a skillet or pan over medium heat. Add the steak; cook on both sides to your desired temperature using a thermometer (see below). Once cooked set aside to rest. Slice against the grain right before serving.
Heat the remaining oil in the same skillet or pan over medium-high heat. Add the mushrooms and sauté until deep golden brown then remove from the pan and set aside.
In the same skillet or pan over medium heat, sauté the garlic and ginger for 2 minutes. Add in the broth, soy sauce, rice wine vinegar, bok choy and bring to a simmer for 10 minutes. Taste and adjust the seasoning with salt and pepper. Remove from the heat and mix in the noodles to warm.
In a bowl, place a serving of noodles, ladle the soup over them. Top with sliced steak and eggs (sliced in half lengthwise). Garnish with scallions.