Add 2 tablespoons oil to a large nonstick pan (or cast iron pan) and heat over medium heat until hot. Add the pork parts. Let cook for 4 to 5 minutes without touching, until the bottom is browned. Flip to brown the other side. It will take 10 to 15 minutes for the whole browning process.
Transfer the browned pork to a 6-quart (5.5-liter) dutch oven (or a heavy-duty pot). Add 10 cups cold tap water to the pot. Cook covered until boiling. Use a fine sieve to skim the brown bits from the top of the soup and discard them.
While boiling the broth, prepare the rest of the ingredients. Combine the dried shrimp with 1 cup warm water. Let rehydrate for 15 minutes or until soft.
Separate the heads of the fresh shrimp from the bodies and peel the shrimp. Reserve the brown bits coming from the heads when you seperate them. This is the best part and adds tons of flavor to the soup. Transfer the shrimp heads to a small bowl, and the rest of the shrimp meat to a container. Store the shrimp meat in the fridge until ready to use (or in the freezer if you plan to serve the noodle soup more than a day from now).
Add 1 tablespoon oil to the same nonstick pan you used to brown the pork. Heat over medium heat until hot. Add the shrimp heads. Cook until both sides turn a deep red color. Transfer heads to the stock pot. Add a ladle of water to the pan you cooked the shrimp in. Scrape off any brown bits stuck on the bottom and pour that water into the stock pot.
Add the remaining 1 tablespoon oil, onion, and garlic to the same nonstick pan. Stir and cook until the edges turns golden brown. Transfer the onion and garlic to the stock pot.
Add the rehydrated shrimp to the nonstick pan. Add a bit more oil if the pan looks too dry. Stir and cook until slightly browned. Transfer the shrimp to the stock pot.
Add the fish sauce, star anise, cinnamon stick, dried chili peppers, white peppercorns, and sugar to the pot. Turn to low heat, cover, and simmer for 2 hours.
Once done, strain the soup by setting up a big bowl (or container) with a fine sieve on the top. Ladle the soup into the bowl through the sieve, a few cups at a time. Use the back of your ladle or a pair of tongs to press the solid ingredients in the sieve, to extract any residual liquid trapped in the veggies and shrimp heads. Discard the all the solid ingredients once done straining.
Taste the soup and adjust the flavor by adding soy sauce or salt. The soup should taste a bit salty by itself, because most of the ingredients in the noodle bowl will be boiled and not seasoned.
Now you can use the soup base to make noodle soup, or store it in the fridge or freezer until read to use. Set the stove on lowest heat to keep the soup hot if you’re going to assemble and serve the bowls immediately.