Cut the chicken breasts into bite-size pieces and season them with the 1/2 teaspoon garlic salt and 1/2 teaspoon paprika.
In a mixing bowl, whisk together 1/2 cup honey, 2 tablespoons soy sauce, 1/2 teaspoon crushed red pepper flakes, 1 tablespoon brown sugar, 1/2 teaspoon paprika, and any remaining garlic salt until smooth.
Heat 1 1/2 tablespoons olive oil in a large skillet over medium-high heat.
Add the seasoned chicken to the hot oil and cook, stirring occasionally, until lightly browned on the outside, about 5 minutes.
Pour the honey sauce into the skillet with the chicken, add the chopped broccoli, and stir to combine.
Continue to cook and stir until the chicken is no longer pink in the center and the sauce has thickened, about 5–10 more minutes.
Serve the honey chicken over white or brown rice, if desired.