Place the chicken thighs in the bottom of the slow cooker and season lightly with salt and pepper.
In a small bowl, stir together the honey, soy sauce, minced garlic, and oregano until well combined.
Pour the sauce mixture evenly over the chicken thighs.
Cover and cook on low for 6 to 7 hours until the chicken is very tender.
About 10 minutes before the chicken is done, bring a pot of water to a boil and add the broccoli florets.
Steam the broccoli for 5 to 7 minutes until it reaches your preferred tenderness, then drain.
Serve the chicken thighs with the steamed broccoli on the side.