Pat the chicken breast dry and cut it into approximately 1-inch pieces. Season with black pepper and salt.
Wash the broccoli, drain it thoroughly, and cut it into bite-sized florets.
In a mixing bowl, whisk together honey, soy sauce, minced garlic, rice vinegar, sesame oil, and optional red pepper flakes.
In a separate small bowl, mix cornstarch with cold water until smooth.
Heat olive oil in a large skillet over medium-high heat. Add chicken in a single layer, cooking in batches if necessary. Brown the pieces for approximately 2–3 minutes per side until nearly cooked through. Transfer to a clean plate.
Add broccoli to the same skillet. Add 1–2 tablespoons of water, cover, and steam for approximately 3–4 minutes until slightly tender. Transfer to a plate if necessary.
Reduce the heat to medium-low. Pour the honey garlic sauce into the skillet and bring it to a gentle simmer.
Stir the cornstarch slurry and gradually add it to the sauce while stirring. Cook for 1–2 minutes until glossy and slightly thickened.
Return the chicken to the skillet and stir to coat. Continue cooking until the thickest pieces reach an internal temperature of 165°F (74°C).
Add the broccoli and gently toss everything together. Heat for another minute, adjust seasoning, and serve immediately.