Heat a large pot or Dutch oven over medium-high heat. Add the ground pork and cook, breaking it up with a wooden spoon, until browned and cooked through (no longer pink), 5 to 7 minutes. Using a slotted spoon, transfer the pork to a plate and set aside, leaving the pork fat in the pot.
Reduce the heat to medium and add the garlic, shallots, and mushrooms. Cook, stirring, until the shallots and mushrooms are tender, 3 to 4 minutes. Add the sesame oil, red pepper flakes, cayenne, and crushed Sichuan peppercorns and cook, stirring often, until the spices are lightly toasted and fragrant, about 1 minute.
Add the miso and stir until well combined. While stirring, gradually pour in 1 cup of the broth and stir until the miso is mixed in well. Pour in the remaining 3 cups broth, the coconut milk, and coconut aminos. Return the cooked pork and any of its juices to the pot. Add the bamboo shoots, green onions, and lime juice. Taste and season with salt and black pepper. Bring the broth to a boil, then reduce the heat to a simmer, cover, and continue to cook while you prepare the eggs and noodles.
Set up a bowl of ice and water and set aside. Bring a medium saucepan of water to a boil. Using a slotted spoon, carefully lower the eggs into the boiling water and cook for 6½ minutes. Transfer the eggs to the ice water to cool.
Add the ramen noodles to the boiling water and cook according to the package directions.
To serve: Divide the cooked ramen noodles among four bowls. Ladle the soup over the noodles. Peel the soft-boiled eggs, halve them, and place them in the ramen. Garnish with the nori strips and toasted sesame seeds.