Pour vegetable oil into a small saucepan or skillet to a depth of about 1/2–3/4 inch. Heat the oil to 350°F (or until shimmering). Add the 4 large shallots (sliced 1/4-inch thick) and fry, stirring often to prevent clumping, until golden brown, about 6–8 minutes. Use a slotted spoon or spider to transfer the fried shallots to paper towels to drain.
In the same oil, add the 3 sliced garlic cloves and fry, stirring, until just barely golden—about 30–60 seconds. Be careful not to burn them. Remove the garlic with a slotted spoon and drain on paper towels. Set the fried shallots and fried garlic aside.
In a small bowl, combine the 2 tablespoons Asian sesame oil with the 2 pressed garlic cloves. Stir and set this sesame–garlic oil aside.
Bring 2–3 quarts low-salt chicken broth to a boil in a large saucepan.
While the broth heats, place the 1 lb chicken (1-inch cubes) in a food processor and pulse until coarsely ground. (If you do not have a food processor, finely chop the chicken.)
Add the coarsely ground chicken to the simmering broth and simmer, stirring and breaking up any clumps with a spoon, until the chicken is cooked through and in small pieces, about 5 minutes.
Use a slotted spoon or spider to transfer the cooked chicken to a large bowl. Add 1 tablespoon of the 4 tablespoons fish sauce to the chicken and toss to coat.
Return the broth to a boil. Add the broken rice stick noodles (maifun) and cook until tender, about 3–4 minutes (follow package timing if necessary). Use a slotted spoon to transfer the noodles to the bowl with the chicken.
Return the broth to a boil again. Add the 8 ounces of green beans/long beans/asparagus (cut into 1-inch pieces) and cook until crisp-tender, about 4–5 minutes. Use a slotted spoon to transfer the vegetables to the bowl with the chicken and noodles.
To the bowl with chicken, noodles, and vegetables add the sesame–garlic oil (from step 3), 1/4 cup fresh lime juice, 1 tablespoon of the raw/brown sugar (from the 2 tablespoons), 2 pinches cayenne pepper, and the remaining 3 tablespoons fish sauce. Toss everything thoroughly to combine and coat evenly.
Transfer the tossed noodle mixture to a large shallow serving bowl. Sprinkle the 1/2 cup chopped fresh cilantro, 1/2 cup chopped green onions, 2 tablespoons chopped salted roasted peanuts, the fried shallots, and the fried garlic over the top. Sprinkle the remaining 1 tablespoon raw/brown sugar over the dish.
Serve immediately, passing hot chili sauce (such as sriracha) at the table for individuals to add to taste.