Heat oil in a large skillet over medium-high. Add minced chicken, breaking it up; cook until no longer pink, about 5–6 minutes.
Push chicken to one side; add garlic and ginger, cook 30 seconds until fragrant. Stir in broccoli and cook 3–4 minutes until bright and tender-crisp.
Mix teriyaki, soy, and sesame oil; pour over chicken and broccoli. Stir to combine.
Add cornstarch slurry, simmer 1–2 minutes until sauce thickens and coats the chicken.
Serve over rice, garnish with sesame seeds and scallions.