To make the marinade, combine all the ingredients in a medium bowl. Add the ground beef, cover and marinate in the refrigerator for about 2 hours. Bring a small pot of water to a boil over high heat, add the eggs and boil for 6 minutes. Drain and immediately dunk in ice water. Peel and set aside.
Cook the ramen noodles according to the package directions, drain and set aside.
To make gravy, melt the butter in a saucepan over medium heat and stir in the flour. Once the roux browns lightly, 1 to 2 minutes, whisk in the beef stock, then the miso. Add the black pepper and salt if needed. Cook for about 6 minutes until the gravy thickens.
Remove the beef from the refrigerator, add to a skillet set over medium-high heat and sauté until cooked through, 2 to 3 minutes.
Divide the noodles among 4 bowls, dress with the miso gravy, then top evenly with the beef, and 1 egg per bowl. Tuck 2 sheets of seaweed next to the rim of each bowl and top with green onions.
