Mince the garlic cloves and cut the broccoli into small, evenly-sized florets—uniform pieces ensure they cook at the same rate. In a medium bowl, whisk together the chicken broth, soy sauce, honey, cornstarch, ginger, sesame oil, and red pepper flakes until the cornstarch is fully dissolved with no lumps. This prevents clumping when the sauce hits the hot pan. Set the sauce aside and have your cut chicken ready nearby.
Heat the neutral oil in a large skillet over high heat until it shimmers. Add the bite-sized chicken pieces in a single layer and let them sit undisturbed for about 1-2 minutes to develop a golden crust—this initial sear builds flavor. Stir and continue cooking for 5 more minutes, stirring occasionally, until the chicken is browned on all sides and cooked through. Transfer the chicken to a clean plate and set aside.
In the same skillet, reduce heat to medium-low and add the minced garlic, stirring for about 30 seconds until fragrant. Add the broccoli florets and pour in the sauce mixture from Step 1, stirring gently to coat everything. Cover the pan and cook for 2-3 minutes, allowing the broccoli to steam and soften slightly while the sauce begins to thicken. I like to keep the heat moderate here so the sauce doesn't break and the broccoli stays vibrant rather than turning mushy.
Return the cooked chicken from Step 2 to the skillet with the broccoli and sauce. Stir everything together gently and cook for 1-2 minutes more, stirring occasionally, until the sauce thickens to a glossy, coat-like consistency and the chicken is warmed through. The cornstarch will continue to thicken as it heats, so watch for the moment when the sauce coats the back of a spoon.
Spoon the chicken and broccoli mixture over freshly cooked white rice in serving bowls. Garnish with sesame seeds if desired for a finishing crunch and visual appeal.