1) Dry brine and season
Pat the chicken dry with paper towels. In a small bowl, mix salt, smoked paprika, garlic powder, onion powder, and black pepper. Sprinkle evenly over all sides of the chicken.
Drizzle with the 1 tablespoon neutral oil and rub to coat (this helps the seasoning stick and encourages browning on the grill or in the oven). Let it sit while you make the sauce, or rest in the fridge uncovered for up to 8 hours if you are planning ahead.
2) Make the BBQ sauce
In a small saucepan over medium heat, stir together ketchup, vinegar, brown sugar, Worcestershire, mustard, smoked paprika, chili powder, cayenne (if using), and salt. Simmer for 3 to 5 minutes, just until glossy and slightly thickened. If it feels too thick to brush, stir in 1 to 2 tablespoons of water.

3) Choose your cooking method
Grill method (best char): Heat the grill for two-zone cooking. Aim for about 400°F on the hot side (medium-high), with the other side on medium-low or off for indirect heat. Lightly oil the grates.
Place chicken skin-side down on the hotter side for 3 to 5 minutes to start browning, then move to indirect heat. Cover and cook, turning occasionally, until the thickest part hits 155°F to 160°F, about 20 to 30 minutes depending on size.
Brush with BBQ sauce, flip, and brush again. Move back over direct heat briefly to set the glaze, 1 to 2 minutes per side. Repeat one more light brushing if you want it extra sticky. Cook until the chicken reaches at least 165°F (safe), or 175°F to 190°F for thighs and drumsticks for best texture. Rest 5 minutes before serving.
Flare-up note: If the skin drips and flames jump, slide the chicken back to indirect heat until things calm down.

Oven method (weeknight reliable): Heat oven to 425°F. Line a sheet pan with foil and set a rack on top if you have one. Arrange chicken skin-side up.
Roast for 20 minutes, then start checking temperature. (Smaller thighs may be ready to glaze sooner.) When the thickest part hits about 155°F to 160°F, brush with BBQ sauce and roast 6 to 8 minutes.
Flip, brush again, and roast 4 to 8 minutes more, until the chicken reaches at least 165°F (or 175°F to 190°F for the most tender thighs and drumsticks). For deeper caramelization, broil for 1 to 2 minutes at the end, watching closely so the sugar does not burn. Rest 5 minutes before serving.

4) Serve
Serve hot with extra sauce on the side for dipping. If you want crispier skin, keep the sauce layers thin and finish with a quick blast of high heat.