In a large bowl, whisk together 3 tablespoons olive oil, garlic, paprika, brown sugar, salt and pepper.

Add the chicken to the bowl, turning a few times to coat evenly with the marinade. Place in the refrigerator for a minimum of 30 minutes or up to 8 hours.

Place an oven rack on the upper middle shelf and preheat the oven to 400 degrees F. Line a rimmed baking sheet with parchment paper or foil. Grease with cooking spray or brush with olive oil.

In a medium-size bowl, toss the potatoes with 1/2 tablespoon olive oil, then spread in a single layer on one side of the prepared baking sheet. (Note: save the bowl for the green beans.) Sprinkle salt and pepper evenly on top.

Remove the chicken from the marinade, discarding the excess liquid. Place onto the center of the baking sheet, leaving space for the green beans. Sprinkle salt and pepper evenly on top.

Roast for 15 minutes. While the chicken and potatoes are roasting, toss the green beans in the remaining 1/2 tablespoon of olive oil.

Carefully remove the baking sheet from the oven. Stir the potatoes, brush approximately half the BBQ sauce over the chicken, and add the green beans to the baking sheet. Sprinkle salt and pepper on top of the beans, then place back in the oven and roast for an additional 10-15 minutes, until the veggies are lightly caramelized and the chicken has reached an internal temperature of 165 degrees F.

Turn the broiler to high. Baste the chicken with the remaining BBQ sauce, then return to the oven until the sauce has cooked onto the chicken and is starting to caramelize, 2-4 minutes (keep an eye on it).