How to Make It
Preheat oven to 425°F. Line a rimmed baking sheet with parchment paper or aluminum foil. Toss potato wedges with 2 tablespoons of the olive oil, 1/2 teaspoon of salt, and 1/4 teaspoon of the smoked paprika.
Spread potatoes in single layer over 1 quarter of prepared baking sheet, and bake in preheated oven until slightly browned and crisp around the edges, about 20 minutes.
Remove baking sheet from oven. Place chicken thighs, skin side up, on half of baking sheet. Sprinkle evenly with pepper, 3/4 teaspoon of the salt, and remaining 1/4 teaspoon smoked paprika. Bake at 425°F until opaque and slightly browned, about 15 minutes.
Toss green beans with lemon zest and remaining 2 tablespoons olive oil and remaining 1/4 teaspoon salt in a large bowl. Remove baking sheet from oven. Place beans in a single layer in remaining quarter of baking sheet. Spoon 1 tablespoon barbecue sauce over each chicken thigh, and return baking sheet to oven. Bake at 425°F until a meat thermometer inserted in thickest part of thighs registers 165°F, about 10 minutes. Serve immediately.