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Peel and finely chop the shallot, garlic cloves and ginger root. Remove the seeds of the chili pepper for a milder version and for an even more milder version you can use only half of the chili pepper and finely chop it.
Fill a small pan with water and the eggs and bring to a boil. As soon as the water starts to boil you boil the eggs for about 6 to 8 minutes, depending how you'd like your eggs.
Remove the ends of the carrots and rinse them well. You can use a sponge or brush to clean the carrots, or peel them with a vegetable peeler instead.
Divide the carrots into slices, not too thick. Rinse the green onion and chop into rings, not too thin.
Heat a large pan on medium-high heat and sauté the shallot, garlic, chili pepper and ginger for a few minutes. Add the carrot along with miso paste.
Pour in the beef stock after about a minute along with a dash of soy sauce and bring to a boil. Meanwhile peel the eggs. Add the noodles after about 5 minutes, make sure they won't stick together so stir them occasionally.
Also add the steaks to the soup and boil it for a few minutes. Make sure they won't overcook and they're still rose in the center, depending how you'd like your steak.
Transfer the beef to a plate and cover with tin foil so they can rest shortly. Add green onions along with sesame oil and mirin. Season with soy sauce and divide the soup over bowls.
Slice the beef with a sharp knife into slices and divide them over the soup along with an egg. Season the eggs with a bit of pepper and enjoy!