Rinse the jasmine rice under cold water until the water runs clear. Combine the rinsed rice and 2 cups of water in a medium saucepan. Bring to a boil over medium-high heat. Reduce heat to low, cover, and simmer for about 15 minutes or until rice is tender and water is absorbed. Remove from heat and let sit covered for 5 minutes.
In a small bowl, whisk together soy sauce, honey, minced ginger, and minced garlic to prepare the teriyaki sauce.
Heat sesame oil in a large skillet over medium heat. Add salmon fillets skin-side down and cook for 4-5 minutes. Flip fillets, pour half of the teriyaki sauce over salmon, and cook for another 3-4 minutes until cooked through and flaky. Remove salmon and set aside.
In the same skillet, add broccoli florets and shredded carrots. Sauté for 3-4 minutes until vegetables are tender but crisp. Drizzle remaining teriyaki sauce over veggies, toss to combine, and cook for an additional minute until heated through.
Assemble the bowls by starting with jasmine rice as the base. Top with sautéed vegetables and place teriyaki salmon on top. Garnish with sliced green onions and sprinkle sesame seeds. Serve immediately.