In a large, deep saucepan bring the vegetable broth to a boil. Add the lemongrass, and cook until you smell the lemony fragrance of the lemongrass. You should start to smell it after about 3-5 minutes. Reduce the heat and add the coconut milk and half the lime juice. Place the salmon fillets in the broth, skin side down. It’s important to leave the skin on the salmon. It imparts loads of flavor to the fish and you can easily remove it before serving.
Cover the saucepan and poach the fish for 10 minutes, until cooked through. You will know the fish is done when you can easily slid a knife into it with no resistance.
While the fish is cooking, in a large saucepan add 2 tablespoons olive oil and garlic and heat it over medium low heat. Be sure to keep a careful watch to make sure the garlic doesn’t brown. After 2-3 minutes add the greens. Cook until wilted and softened. Season to taste with salt, pepper and red pepper flakes.
When the fish is cooked through remove it from the broth and set aside. Cover lightly with tinfoil to keep warm.
Continue cooking the broth for another 1-3 minutes, adding the anchovies (or fish sauce) until it thickens to a consistency that you like. Season with salt and pepper. Taste to double check the seasoning. Feel free to add more anchovy/anchovy paste or fish sauce. This is also the perfect time to add more lime juice, too.
To plate the dish, add the cooked greens to a large deep platter. Place the fillets over the greens, and pour the broth over the salmon and greens. Drizzle the remaining lime juice over the salmon and serve with extra lemon or lime wedges.