Scoop the thick coconut cream from the top of just one of the cans into a large stockpot over medium-high heat. Melt the cream, add the curry paste and stir for a few minutes until they begin to sizzle.
Add the cilantro roots and chicken and sauté until the chicken is cooked through, about 5 minutes.
Add the coconut juice from the first can and all the contents of the second can along with the chicken broth, carrot, lime leaves, lemon grass, fish sauce and lime zest and juice. Grate the ginger into the broth. Simmer for 20 minutes or so.
Stir in the bean sprouts. Add the rice noodles, gently pushing them beneath the surface of the broth. Turn off the heat and let stand until the noodles soften, about 5 minutes. Rice noodles don’t need to simmer like pasta to cook; they simply need to rehydrate in the hot liquid.
Stir in most of the cilantro leaves. Remove the lemon grass stalks. Taste and season with more salt (or soy sauce) as needed. Ladle into large bowls and garnish with the green onions and remaining cilantro leaves.