Make a peanut sauce: Pour the honey, peanut butter, soy sauce and Worcestershire sauce into a large bowl along with the cayenne pepper, garlic, lime juice and 1/4 cup of olive oil. Season with a pinch of salt and pepper, then whisk together. Reserve 1/2 cup in a small bowl for serving.
Add the chicken thighs and drumsticks to the large bowl with the remaining sauce and toss to coat. Cover and refrigerate for 30 minutes.
Preheat the oven to 450 degrees F and line a baking sheet with foil. Remove the chicken from the marinade and place on the baking sheet.
Add the broccoli to a bowl and toss with the remaining tablespoon olive oil, 1 teaspoon salt and a few grinds of pepper. Place on the sheet pan with the chicken, then bake until the broccoli is tender and golden brown in spots, the chicken is crisp and the internal temperature is 165 degrees F, about 30 minutes. Serve the chicken with the broccoli and rice. Sprinkle with the scallions and serve with the lime wedges and reserved peanut sauce.