Season the chicken. Season the chicken breasts all over with kosher salt. Refrigerate for at least 2 hours or up to overnight.
Cook the aromatics. Heat 2 tbsp of coconut milk in a medium pot over medium-low heat. Add the scallions, garlic, ginger and turmeric. Cook, stirring frequently, until fragrant, about 2–3 minutes.
Poach the chicken. Add the chicken, remaining cup coconut milk, chicken stock, soy sauce and fish sauce. The chicken should be submerged; add more broth if needed. Slowly bring to a very gentle simmer, then reduce the heat to low. Cook gently until the thickest part of the chicken registers 165°F, about 20–30 minutes, depending on thickness. The broth should be around 160-170°F, avoid boiling or the chicken might turn out chewy. Transfer the chicken to a plate and set aside.
Cook the noodles. Now bring the broth to a boil. Add the pasta and cook 2-3 minutes shorter than the package instructions indicate, stirring occasionally to prevent sticking.
Finish. Stir in the spinach until wilted, then remove the pot from the heat. Squeeze in the lime juice, taste and adjust the seasoning.
Serve. Slice or shred the chicken and divide among bowls, add the noodles and spoon over the broth. Top with cilantro and lots of fried shallots. Serve with lime wedges.