Rinse jasmine rice until water runs clear. In a medium pot, combine rice, coconut milk, and water. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes until rice is tender and liquid is absorbed.
While rice cooks, pat salmon fillets dry with paper towels and season with salt and pepper on both sides.
In a small bowl, whisk together soy sauce, 1 tablespoon sesame oil, ginger, garlic, and honey to create a glaze.
Heat remaining 1 tablespoon sesame oil in a large skillet over medium-high heat. Place salmon skin-side up in the pan and cook for 4 minutes.
Flip salmon, brush with half the glaze, and cook for another 4-5 minutes until salmon flakes easily with a fork.
Fluff coconut rice with a fork and divide among four bowls. Top each with baby spinach, shredded carrots, and a salmon fillet.
Drizzle remaining glaze over the bowls and garnish with green onions and sesame seeds before serving.