Season the chicken thighs with about half of the fine sea salt and all of the freshly ground black pepper, tossing the strips so they are evenly coated.
Heat the neutral oil in a large pot or Dutch oven over medium-high heat until shimmering.
Add the seasoned chicken strips to the hot oil in a single layer and cook, stirring occasionally, until lightly browned on the outside and just cooked through, about 5 to 7 minutes.
Reduce the heat to medium, push the chicken to one side of the pot, and add the unsalted butter to the empty side.
Once the butter has melted, add the minced garlic and grated ginger to the buttered side and sauté, stirring constantly, until fragrant, about 30 to 45 seconds, without letting them brown.
Stir the garlic and ginger mixture into the chicken, then pour in the soy sauce, sriracha, chili garlic sauce, and rice vinegar, stirring to coat the chicken evenly.
Pour the chicken broth and water into the pot, add the remaining fine sea salt, and stir well, scraping up any browned bits from the bottom of the pot.
Bring the mixture to a gentle boil over medium-high heat, then reduce the heat to medium-low and let the broth simmer for 8 to 10 minutes to allow the flavors to meld.
Stir in the coconut milk until fully combined, then let the broth return to a gentle simmer without boiling hard.
Add the instant ramen noodles to the pot, gently pushing them down into the broth, and cook according to package directions, usually 3 to 4 minutes, until just tender.
During the last 2 minutes of cooking the noodles, add the sliced green cabbage and shredded carrot to the pot and stir them into the broth.
Turn off the heat and stir in the toasted sesame oil, tasting the broth and adjusting seasoning with a little more salt if needed.
Ladle the spicy and creamy chicken ramen into bowls, making sure each serving has a mix of broth, noodles, chicken, cabbage, and carrot.
Top each bowl with sliced green onions, half of a soft-boiled egg, toasted sesame seeds, and a pinch of crushed red pepper flakes if using, then serve immediately while hot.