Add the rice and water to a medium saucepan. Bring to a boil, then lower the heat, cover, and simmer for 15 minutes until the water is absorbed.
While the rice cooks, stir together the honey, soy sauce, and minced garlic in a small bowl to make the glaze.
Heat the olive oil in a large skillet over medium heat. Season the salmon with salt and pepper, then place it skin-side down in the skillet. Cook for 4 minutes.
Flip the salmon and pour the glaze over the fillets. Cook 3 more minutes, spooning the glaze over the fish as it thickens.
Add the broccoli florets to the skillet around the salmon. Cover and steam for 4 minutes until the broccoli turns bright green and tender.
Remove the skillet from the heat. Fluff the rice and divide it among four plates. Top each plate with one salmon fillet and a portion of broccoli. Sprinkle with sesame seeds and green onions before serving.