In a small bowl, mix together the dry spices: smoked paprika, garlic powder, onion powder, chili powder, salt, pepper, and if you like it hot, a few big pinches of cayenne pepper.
Toss the chicken pieces in a large bowl with the olive oil. Coat with the spice mix. Cover and marinate for 1 hour in the fridge.
When ready to cook the chicken, pre-heat oven to 425 degrees F. Toss the broccoli pieces in a little olive oil and sprinkle with Kosher salt.
On a large sheet pan, spread out the marinaded chicken pieces on one half of the pan. Leave room between the pieces. Add the broccoli on the other half.
Bake for 12-14 minutes. Stir the broccoli around halfway.
Brush the chicken pieces with the BBQ sauce and roast for another 5 minutes or until the chicken is 165 degrees F.