Preheat the oven to 300 degrees. Generously salt and pepper the pork shoulder and then heat vegetable oil in a dutch oven over medium heat. Add the pork shoulder and sear on each side until dark brown, about 8 minutes per side. Make sure to let the fatty sides really interact with the oil/heat. Take out the pork shoulder and put aside on a plate.
Add the ginger and garlic heads (you can put them in whole w/ the wrapper) and let it get fragrant, about 4 minutes. Add the soy sauce, fish sauce, rice vinegar, and 4 cups water and bring to a simmer. Once simmering, add in the pork shoulder. Make sure the liquid covers about 3/4 of the pork (add more water if it doesn't), and then put the covered dutch oven the oven. Roast the pork for about 3 hours, or until tender (but doesn't totally fall apart/shred.)
Heat the ramen broth in a large pot over medium low heat. Add the gochujang and sriracha and let simmer. Taste the broth and season to taste (more spice, more salt, etc.)
Add bok choy, corn, and any other veggies of your choice to the broth.
Add the ramen noodles to the pot of simmering ramen broth, let simmer for the amount of time required based on ramen instructions.
Once pork shoulder is done, take out of dutch oven and slice in 1-inch pieces. If you'd like, you can use some of the pork broth and add to the ramen broth for additional flavor and volume.
Assemble the bowls by adding the soup to the bowls and topping with pork shoulder, lime, jammy eggs, crispy shallots, and chili oil.