Rinse the jasmine rice under cold water until the water runs clear. In a medium saucepan, combine the rice with 2 cups of water and a pinch of salt. Bring to a boil, then reduce the heat to low, cover, and simmer for about 15 minutes or until the water is absorbed and the rice is tender. Remove from heat and let it sit, covered, for 5 minutes.
In a small bowl, whisk together the soy sauce, honey, rice vinegar, sesame oil, grated ginger, and minced garlic until well combined.
Heat a non-stick skillet over medium-high heat. Season the salmon fillets with salt and pepper. Place the fillets skin-side down in the skillet and cook for 4-5 minutes. Flip the salmon fillets and pour half of the teriyaki sauce over them. Cook for another 3-4 minutes, basting with the sauce until the salmon is cooked through and flakes easily with a fork.
In a separate pan, add a splash of sesame oil. Add the mixed vegetables and stir-fry for about 3-4 minutes until they are vibrant and tender-crisp.
Fluff the cooked rice with a fork and divide it evenly among serving bowls. Top each bowl with the stir-fried vegetables and a salmon fillet. Drizzle the remaining teriyaki sauce over the salmon and vegetables.
Sprinkle sesame seeds and sliced green onions on top for garnish. Serve immediately and enjoy your flavorful teriyaki salmon rice bowl!