Blanch the Bones: Place pork neck bones and chicken carcasses in a large pot. Cover with cold water and bring to a rolling boil over high heat. Boil for 5 minutes, then drain, rinse bones under cold water, and clean the pot.
Char the Aromatics: Place halved onion and sliced ginger cut-side down in a dry skillet over medium-high heat. Char until dark brown, about 3 to 4 minutes per side. Smash garlic cloves flat with the back of a knife.
Build the Broth: Return blanched bones to the clean pot. Add charred onion, ginger, smashed garlic, and scallions. Pour in 12 cups of cold water. Bring to a boil over high heat.
Simmer Low and Long: Reduce to a vigorous simmer. Cook for 3 to 4 hours, skimming foam during the first 30 minutes. Add water if the level drops below the bones.
Make the Tare: Combine soy sauce, mirin, and sake in a small saucepan over low heat. Stir in miso paste if using. Warm for 2 minutes without boiling. Set aside.
Strain and Season: Strain the broth through a fine mesh sieve into a clean pot. Discard solids. Taste and adjust with salt or extra soy sauce as needed.
Assemble the Bowls: Add 1 to 2 tablespoons of tare to each serving bowl. Ladle in hot broth. Add cooked ramen noodles and desired toppings. Drizzle with sesame oil and serve immediately.
