In a large resealable plastic bag, combine chicken and ¼ cup cornstarch; season with salt and pepper and shake bag to coat.
In a large skillet or wok over medium-high heat, heat 2 tablespoons oil. Shake off excess cornstarch and add chicken to oil. Working in batches, cook chicken, turning occasionally, until golden brown, about 7 minutes. Transfer to a paper towel-lined plate.
In same skillet over medium heat, heat remaining 1 tablespoon oil. Add garlic and red pepper flakes cook, stirring, until fragrant, about 30 seconds. Add broth, scraping any brown bits with a wooden spoon.
In a medium bowl, whisk soy sauce, hoisin sauce, honey, lime juice, and remaining 1 tablespoon cornstarch until combined. Add to skillet and simmer, tossing constantly, until slightly thickened, about 1 minute.
Add broccoli and cook, tossing, until tender, about 5 minutes. Return chicken to skillet and stir to coat. Cook, tossing, until warmed through, about 1 minute more.
Divide rice among bowls. Top with chicken and sesame seeds.
