Cook the Rice: Bring 1 ½ cups vegetable stock to a boil in a medium saucepan over medium-high heat. Stir in the jasmine rice, ¼ cup of the shallots, and ½ teaspoon of the salt. Reduce the heat to low, cover, and cook for about 15 minutes.
Build the Poaching Base: While the rice cooks, add the leeks, the remaining ¼ cup shallots, the ginger, and another ½ teaspoon of the salt to a large deep skillet over medium heat. Cook for about 2 minutes, stirring often, until the vegetables begin to soften.
Add the Liquid: Pour in the coconut milk and the remaining 1 ½ cups vegetable stock. Stir in the crushed red pepper and bring the mixture to a gentle simmer over medium-low heat.
Season the Salmon: Sprinkle the salmon fillets with the remaining ½ teaspoon salt.
Poach the Salmon: Place the salmon fillets into the simmering coconut mixture in a single layer. Keep the heat low to medium-low so the liquid stays at a gentle simmer, and cook for 6 to 8 minutes, until the salmon is opaque and flakes easily.
Set Aside the Salmon: Carefully lift the salmon out with tongs or a fish spatula and transfer it to a plate.
Cook the Vegetables: Add the frozen Asian vegetable mix to the skillet with the coconut poaching liquid. Simmer over medium heat for 3 to 5 minutes, stirring occasionally, until the vegetables are heated through and tender-crisp.
Finish the Rice: Once the rice is done, remove it from the heat and let it sit covered for about 5 minutes if needed. Fluff with a wooden spoon.
Serve the Dish: Spoon the rice onto plates, top with the vegetables, and place a salmon fillet on each serving. Spoon some of the coconut broth over the top and serve warm.