This was a fun recipe to make, if complicated. I made it ahead and kind of over-reduced it a bit (and my noodles turned out a little clumpy), but overall we really liked it.
1 whole dried Thai bird chili
2 whole small shallots, peeled and split into quarters
4 whole cloves garlic
1 stalk lemongrass, bottom 4 inches only, roughly chopped
1 teaspoon makrut lime zest, or 2 whole makrut lime leaves
1 (1-inch) knob fresh turmeric, roughly chopped
2 thin slices ginger
1 small bunch cilantro stalks
1 teaspoon whole coriander seed
1 pod green cardamom, inner seeds only
1 1/2 tablespoons Thai shrimp paste
1 cup vegetable or canola oil
1 pound fresh Chinese-style egg noodles, divided
2 (15-ounce) cans coconut milk
1 cup homemade or store-bought low-sodium chicken stock
2 tablespoons palm sugar (I used coconut sugar)
4 chicken legs, split into drumsticks and thighs (I used drumsticks and thighs already separated)
Fish sauce to taste
Sliced shallots, lime wedges, and pickled Chinese mustard root (I couldn’t find these, but added some cilantro and fried shallots) for serving
Place chili, shallots, garlic, lemongrass, lime zest, turmeric, ginger, cilantro stalks, coriander seed, and cardamom in the center of a 12- by 12-inch square of heavy duty aluminum foil. Gather edges up to make a tight pouch. Place pouch directly over the flame of a gas burner and cook, turning occasionally, until aromatic and wisps of smoke begin to rise, about 8 minutes. If no gas burner is available, place the pouch in the bottom of a wok or cast iron skillet and heat over high heat, turning occasionally, until smoky, about 10 minutes. Allow contents to cool slightly and transfer to a large mortar and pestle (I did this in the food processor instead).
Add a large pinch of salt to the aromatics. Pound until a very fine paste is formed, about 10 minutes. Add shrimp paste and pound to incorporate. Set curry paste mixture aside.
Separate out 1/4 of the noodles (enough noodles to make a crispy fried-noodle topping for 4 bowls) and set the remaining noodles aside. Heat vegetable oil in a large wok over high heat until shimmering. Working in batches, add noodles to oil and fry, stirring and flipping until golden brown and crisp. Transfer to a paper towel-lined plate. Season with salt and set aside.
Discard all but 1 tablespoon oil from wok. Using a spoon, skim 2 tablespoons of creamy fat off the top of the coconut milk and add to the wok. Heat wok over high heat and cook, stirring constantly, until coconut milk breaks and oil begins to lightly smoke, about 2 minutes. Add curry paste mixture and cook, stirring and smearing the paste into the oil, until aromatic, about 45 seconds.
Slowly whisk in the coconut milk, followed by the chicken stock and palm sugar. Add chicken legs and bring to a simmer. Cook, turning chicken occasionally, until chicken is tender and broth is very flavorful, about 30 minutes. Season to taste with fish sauce.
Bring a pot of salted water to a boil. Add remaining uncooked noodles and cook until al dente, about 1 minute. Drain noodles and divide between four warmed bowls. Top noodles with two pieces of chicken. Divide broth evenly between bowls. Top with fried noodles and serve immediately with sliced shallots, lime wedges, and pickled mustard greens on the side.