Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the carrots into thin rounds and toss them on the baking sheet with olive oil, 0.25 tsp sea salt, and 0.125 tsp black pepper.
Roast the carrots for 20-25 minutes, turning halfway through, until they are tender and show caramelized edges.
While carrots roast, combine the coconut milk, water, grated ginger, minced garlic, and the remaining salt and pepper in a medium skillet.
Bring the liquid to a very gentle simmer over medium-low heat; do not let it reach a rolling boil.
Place the salmon fillet skin-side down into the poaching liquid, cover with a lid, and cook for 8-10 minutes until the fish is opaque and flakes easily with a fork.
Carefully remove the salmon from the skillet and stir the fresh lime juice into the remaining coconut liquid to create a light sauce.
Serve the salmon over the roasted carrots and finish by drizzling the warm ginger-coconut sauce over the top.