Preheat the oven to 400F (200C). Line a large baking sheet with parchment paper and set aside.
Place the barbecue sauce with honey and hot chili sauce into a small saucepan. Simmer over low heat for 1-2 minutes. Remove from heat and set aside.
Cut potatoes into about 1 inch (2.5 cm) chunks. Add potatoes and sweet potatoes to a large bowl. Add olive oil, salt, pepper, herbs, garlic powder, breadcrumbs and Parmesan cheese over the potatoes. Toss to coat.
Arrange the tossed potatoes on the baking sheet on one side.
Cut broccoli into florets and place into a large bowl. Drizzle with a bit of olive oil, season with salt and pepper and toss to coat.
Place the chicken and broccoli on the baking sheet. Season chicken breast with salt, pepper and smoked paprika if used.
Brush the chicken with honey BBQ sauce.
Bake for 25-30 minutes until veggies are tender and chicken is cooked through.
If broccoli cooks too fast, cover it with aluminum foil after the first 15 minutes.
Broil for a few minutes before removing the baking sheet from the oven.
Once it has finished baking remove the pan from the oven and add a bit more honey BBQ sauce to the chicken if desired.