In a mixing bowl, stir together the honey, soy sauce, minced garlic, olive oil, ground ginger, salt, and black pepper until the mixture is smooth.
Place the chicken thighs in the slow cooker and pour the honey garlic mixture evenly over them.
Cover and cook on low for 6 hours or on high for 3 to 4 hours until the chicken is tender and cooked through.
About 10 minutes before the chicken is done, bring a pot of water to a boil and add the broccoli florets to a steamer basket. Steam for 5 to 7 minutes until the broccoli is bright green and tender but still firm.
Serve the chicken thighs with the sauce from the slow cooker alongside the steamed broccoli.