Combine 1 cup long-grain white rice and 2 cups water in a medium saucepan; bring to a boil.
Reduce heat to low, cover, and simmer for 15–18 minutes until water is absorbed and rice is tender.
Remove from heat and let sit, covered, for 5 minutes; fluff with a fork.
Meanwhile, cut 1 pound boneless, skinless chicken breast into 1-inch pieces; slice 1 large carrot thinly and prepare 3 cups broccoli florets.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add chicken and cook 5–7 minutes, stirring occasionally, until golden and cooked through to 165°F. Transfer chicken to a plate.
Add broccoli and carrots to the same skillet (add more oil if needed) and sauté 3–5 minutes until crisp-tender.
Return chicken to the skillet with vegetables.
Whisk together 1/4 cup low-sodium soy sauce, 2 tablespoons honey, 1 tablespoon rice vinegar, 1 teaspoon grated fresh ginger (or ground ginger), 1 clove minced garlic (or garlic powder), and 1 tablespoon cornstarch.
Pour sauce over chicken and vegetables; cook 1–2 minutes, stirring constantly, until sauce thickens and coats everything.
Divide rice among four bowls and top with the chicken & vegetable mixture.
Garnish each bowl with sesame seeds and sliced green onions; serve immediately.