Season steak slices with kosher salt and black pepper.

Heat 1 tablespoon of olive oil in a large pot over medium-high heat and sear the beef slices for 1-2 minutes per side.

Remove the beef from the pot and set aside.

In the same pot, add remaining oil, minced garlic, and ginger; stir-fry for 3 minutes.

Add sliced shiitake mushrooms and cook for another 2-3 minutes.

Pour in beef broth, coconut aminos (or soy sauce), and fish sauce; bring to a gentle simmer for 10 minutes.

While the broth simmers, boil water in a small saucepan and cook the eggs for 4-5 minutes, then transfer to an ice bath.

Cook the ramen noodles according to package instructions.

In four bowls, divide the noodles, ladle the hot broth over, and top with seared beef, soft-boiled egg halves, and sprinkle with green onions.

Serve with lime wedges.