Wipe the mushrooms clean, trim the stalks, halve any larger mushrooms, then dry char in a large non-stick casserole pan on a medium heat for 5 minutes, or until dark golden and beautifully nutty, turning halfway.
Meanwhile, peel the carrots and finely slice into rounds at an angle. Trim and roughly slice the scallions. Drain the tofu and chop into eight chunks.
Pull the skin off the chicken thighs and discard. Use the heel of a large knife to cut each thigh through the bone into three pieces by carefully and firmly tapping the knife with a rolling pin—this will add more flavor to the broth.
Remove the mushrooms to a plate, and add the chicken and carrots to the pan. Cook for 10 minutes, stirring regularly.
Pour in the stock, bring to a boil, then simmer for 20 minutes.
Stir in the scallions, mushrooms, tofu, soy sauce, and chili paste and simmer for a final 20 minutes.
Chop the kimchee and stir through just before serving (this means it isn’t overexposed to heat, so will retain more of its nutritional benefit).
While the soup is simmering, cook the noodles according to the package instructions, then drain. Toss with the sesame oil and seeds, and divide between your bowls.
Taste the broth, season to perfection, then squeeze in lime juice to add contrast. Divide between your hot noodle bowls, and enjoy.