With a broth that boasts the rich, fragrant, deep flavor of a long-cooked stock and the prep and cook time of about an hour, ramen doesn’t get easier than this. There’s a wee bit of mirin (rice wine) in this dish; if you prefer to avoid the residual sugar, use 1 tablespoon rice wine vinegar...
Preheat the oven to 375°F (190°C). Season the chicken generously with salt and pepper.
In a large, deep sauté pan over medium heat, melt the coconut oil. Add the chicken, skin-side down, and cook until the skin is golden brown and releases easily from the pan, 5 to 6 minutes. Flip and cook, 4 minutes more.
Transfer the chicken to a baking dish, reserving the pan and its drippings, and roast until the chicken is cooked through, 15 to 18 minutes. Transfer to a plate.
Meanwhile, heat the pan with chicken drippings over medium-high heat. Add the bok choy, cut side down, and cook until it has a golden brown sear, 4 to 5 minutes. Add 1 tablespoon of the soy sauce, toss to coat, cover the pot and cook until soft when poked with the tip of a paring knife, 4 to 5 minutes. Transfer to a plate and cover to keep warm.
Heat the same pan over medium heat. Add the ginger and garlic and cook until softened 3 minutes. Stir in the remaining ¼ cup soy sauce and the mirin. Cook for 1 minute. Add the broth, cover, bring to boil, then remove the lid and let gently simmer, uncovered, for 10 minutes more. Season to taste with salt.
Fill a medium bowl with ice water. Fill a pot with enough water to cover the eggs (don’t add the eggs yet). Bring to a boil. Gently lower the eggs into the boiling water, lower the heat, then let simmer for 8 minutes. Immediately transfer the eggs to the ice water. Cool until cool enough to handle, 5 minutes. Carefully peel and halve the eggs lengthwise. Set aside.
To serve, slice the chicken into thin pieces. Divide the noodles into four large bowls. Add the sliced chicken and hot ramen broth. Top with bok choy, radish slices, and soft-boiled eggs. Garnish with sesame seeds and chili sauce.