Preheat oven to 400°F and line a large sheet pan with foil.
Whisk together honey, soy sauce, garlic, olive oil, paprika, salt, and pepper in a small bowl.
Pat chicken thighs dry and place skin-side up on the sheet pan, then spoon the sauce generously over each piece.
Roast for 25 minutes, then add broccoli florets around the chicken and spoon any pan drippings over the broccoli.
Return to oven for 15 more minutes until chicken skin is deeply golden and an internal thermometer reads 165°F.
Spoon remaining pan sauce over everything before serving.