Heat the sesame oil in a large pot over medium heat, until shimmering. Add the garlic and ginger, and cook for a few minutes being careful not to brown
Add the miso, soy sauce and mirin, and stir to combine. Cook for another minute. Add the chicken stock and white parts of the scallions and bring to boil and then lower to a simmer for 10 minutes. Season with salt, to taste. This will vary depending on the chicken stock that you use.
In the meantime, make the soft-boiled eggs: Fill a small pot with enough water to cover the eggs, and bring to a boil. Gently lower the eggs into the boiling water, and let simmer for 7 minutes (for a slightly-runny yoke) or 8 minutes (for a soft, but set-up yoke).
Meanwhile, fill a large bowl with ice water. When the timer finishes, transfer the eggs to the ice bath to stop the cooking process. Do not dump out the water! You will use this to cook your ramen noodles. When the eggs are cool enough to handle, carefully peel off the shell and slice in half, lengthwise. Set aside until ready to serve.
Add the ramen noodles to the boiling water (from cooking the eggs.). Cook for 2-3 minutes, until soft, then divide the noodles into four large bowls. Add the broth. Top with the fresh scallions, sesame seeds and the soft-boiled egg. Serve immediately.