Make the Coconut Broth: Combine the vegetable stock, coconut milk, minced ginger, shallot, garlic, lime zest, lemongrass, and ½ teaspoon Kosher salt in a medium saucepan. Bring the mixture to a boil over high heat.
Simmer the Broth: Once boiling, reduce the heat to medium-low and gently simmer the broth for 30 minutes, allowing the aromatics to infuse the liquid.
Strain the Broth: Pour the finished broth through a strainer into a bowl, removing and discarding the solids. Set the strained broth aside.
Prepare the Salmon: Pat the salmon filets dry with paper towels, remove any residual bones, and cut the fish into 1-inch cubes. Season evenly with ½ teaspoon Kosher salt and 1 teaspoon freshly ground black pepper. Sauté the Vegetables: Heat 1 tablespoon coconut oil, or olive oil, in a stock pot over medium heat. Add the diced onion and bell pepper and cook, stirring frequently, for 4–5 minutes, until the vegetables become translucent. Add the Aromatics: Stir the grated ginger and finely minced garlic into the sautéed vegetables. Cook for approximately 1 minute, stirring, until the aromatics are incorporated.
Build the Soup: Pour the reserved coconut broth into the stock pot and add the second 13.5-ounce can of full-fat coconut milk. Bring the soup to a boil.
Simmer the Soup: Reduce the heat as needed and let the soup simmer for 15 minutes so the flavors come together.
Add the Broccoli: During the final 5 minutes of the 15-minute simmer, add the rinsed, finely cut broccoli florets and allow them to cook in the soup.
Add the Salmon: At the very end of the cooking time, add the seasoned salmon cubes and cook for 1 minute. Then immediately turn off the heat, allowing the residual heat to continue cooking the salmon. Balance the Flavor: Stir in the freshly squeezed lime juice and maple syrup. Taste the soup and adjust the seasoning as needed, adding more lime juice or maple syrup if desired.
Garnish and Serve: Finish the soup with sliced scallions, sliced jalapeño, and roughly chopped or torn fresh cilantro leaves. Serve immediately with the quartered lime wedges on the side.