Rinse the jasmine rice under cold water until the water runs clear. In a rice cooker or pot, combine the rice and 2 cups of water. Cook according to the rice cooker's instructions or bring to a boil, then cover and reduce heat to low for 15 minutes until all the water is absorbed. Remove from heat and let it sit covered for another 5 minutes.
While the rice is cooking, prepare the sauce. In a bowl, mix together the soy sauce, honey (or maple syrup), sesame oil, grated ginger, and a pinch of salt and pepper. Set aside.
Heat a non-stick skillet over medium-high heat. Season the salmon fillets with salt and pepper on both sides. Once the skillet is hot, place the fillets skin-side down. Cook for about 5-6 minutes without moving them until the skin is crispy.
Flip the fillets carefully and cook for another 2-3 minutes until the salmon is cooked through and flakes easily with a fork.
In the last few minutes of cooking the salmon, steam the broccoli florets and carrot in a small pot with a little water until they are tender but still crisp, about 3-4 minutes.
To assemble the rice bowls, divide the cooked rice between two bowls. Top each bowl with one salmon fillet, the steamed veggies, and the sliced cucumber.
Drizzle the sauce over the top and sprinkle with chopped green onions and sesame seeds. Add chili flakes if desired.
Serve immediately while the salmon is still warm.