Bring a small pot of water to a boil and carefully lower in the egg; cook for 6.5 minutes, then immediately transfer to an ice bath to stop the cooking.
In a large saucepan or Dutch oven, heat the toasted sesame oil over medium-high heat.
Add the ground pork, sea salt, and black pepper to the pan, browning the meat and breaking it into small crumbles until fully cooked.
Stir in the minced ginger and garlic, sautéing for about 1 minute until fragrant but not browned.
Pour in the chicken bone broth, tamari, and sriracha, bringing the mixture to a gentle simmer.
Add the brown rice ramen noodles and chopped baby bok choy to the broth, simmering for 3 to 4 minutes until the noodles are tender and the greens are wilted.
Carefully peel the cooled egg and slice it in half lengthwise.
Ladle the soup and pork into a deep bowl, then top with the soft-boiled egg halves and a garnish of sliced green onions.