Pat the salmon filets dry. Season with salt and pepper, to taste.
In a large skillet, heat the avocado or coconut oil over medium-high heat. Sear the flat side first, undisturbed, about 6-7 minutes until browned. It will release easily from the pan once it's ready to be flipped.
Flip and sear for 4-5 minutes more. Remove from the pan and set aside. They do not have to be cooked through; they will fully cook in the sauce later.
Reduce the heat to medium-low and add sesame oil. Sauté shallots until softened, stirring often, about 2 minutes. It will foam up and that's ok. That's just the liquid from the salmon.
Add in the garlic and ginger. Sauté for 1 minute until fragrant, stirring continuously. Stir in the brown sugar and cook until it has caramelized, stirring constantly so it doesn’t burn. Stir in sriracha. It will splatter, so be careful!
Pour in the coconut milk and stir, gently scraping the bottom of the skillet to lift browned bits to incorporate in the sauce. Stir in soy sauce and fish sauce. Increase the heat to medium, and simmer 5-7 minutes.
Place the salmon into the skillet, and reduce the heat to medium-low. Bring to a light simmer and cover. Simmer for 6-8 minutes, or until the salmon is cooked through (145F). Remove salmon with a fish spatula or equivalent to a plate.
Stir in the lime juice and zest, then simmer for 2 more minutes. Turn off the heat. Taste and adjust seasoning with salt and pepper as needed.
Serve over rice or noodles, garnish with cilantro and chiles, and serve with a lime wedge.