Heat broiler. In a small bowl, combine the sugar, soy sauce, and garlic. Set aside.
Cook the rice according to the package directions, using vegetable broth instead of water, stir in the broccoli and edamame during the last 3 minutes.
Let the rice and broccoli stand off the heat until the broccoli is tender, about 5 minutes. Fluff with a fork.
Meanwhile, place the salmon on a rimmed baking sheet. Drizzle with the olive oil and season with salt and pepper.
Broil until the salmon is opaque throughout, 8 to 10 minutes, spooning half the soy sauce glaze over the fish during the last 2 minutes of cooking.
Serve the salmon with the rice and the remaining glaze.