Heat sesame oil in a large cast iron skillet over medium-high heat.
Add chicken and cook for 5 minutes, stirring occasionally.
Add garlic, ginger, and red pepper flakes and cook for 1 minute.
Add chicken broth, soy sauce, and honey and stir to combine.
Add broccoli and cook for 5 minutes, stirring occasionally.
Add almonds and cook for an additional 2 minutes, stirring occasionally.
Serve hot with steamed rice or noodles.