Cook the rice according to package directions in a medium saucepan. Keep it warm once finished.
Heat one tablespoon of oil in a large skillet over medium heat. Add the salmon fillets and cook for 4 minutes on the first side.
Flip the salmon, pour half the teriyaki sauce over the fillets, and cook for another 3 to 4 minutes until the fish flakes easily. Remove the salmon to a plate.
Add the remaining tablespoon of oil to the same skillet. Stir in the garlic and ginger and cook for 30 seconds.
Add the broccoli, bell pepper, and carrots. Stir-fry for 5 minutes until the vegetables are crisp-tender.
Return the salmon to the skillet, drizzle with the remaining teriyaki sauce, and heat everything together for one minute.
Divide the rice among four bowls. Top each with salmon and vegetables. Finish with sliced green onions and sesame seeds.