Season salmon filets on flesh and skin side with salt. Combine coconut milk, broth, lime juice, and fish sauce in a small bowl.
Heat oil in a frying pan over medium heat. When the oil is warm sear salmon in pan 2 minutes each side and remove from the pan. Add minced garlic and chili flakes to the warm pan and cook for 3-4 minutes.
Pour in the coconut milk mixture and increase heat to medium high until sauce bubbles. Reduce heat to medium low and simmer the sauce for 5 minutes and then add the seared salmon back to the pan with skin side up. Poach salmon in the simmering sauce for 6 minutes keeping the skin side up the whole time and regularly spooning sauce over the skin side of the salmon. Remove the poached salmon from the sauce.
Combine arrowroot flour and water in a small bowl. Increase the heat of the sauce to medium and pour starch and water slurry into the sauce while you're stirring the sauce. Continuing stirring the sauce until the mixture thickens- about 2 minutes.
Turn off the heat, but leave the frying pan on the stove. Place salmon filets back in the sauce and cover with thickened sauce. Garnish with lime zest and cilantro and enjoy!
This nutritional information refers to each serving of the entire recipe and not just the products used as ingredients.