Preheat the Oven: Set oven to 400°F and line a large sheet pan.
Make the Spice Mix: In a small bowl, combine salt, pepper, garlic powder, oregano, and smoked paprika. Divide into two portions.
Season the Carrots: Toss carrots with 1 tbsp olive oil and half the spice mix. Spread evenly on the sheet pan.
Season the Chicken: Toss chicken with remaining olive oil and the rest of the spice mix. Place on the sheet pan next to the carrots. Add lemon halves cut-side down.
Roast: Bake for 25–30 minutes until chicken is fully cooked and carrots are tender and slightly caramelized.
Make the Sauce: In a bowl, mix Greek yogurt, cilantro, olive oil, black pepper, garlic powder, and salt. Squeeze in juice from the roasted lemon and whisk until smooth.
Assemble: Serve chicken and carrots over cooked rice. Drizzle generously with lemon yogurt sauce and garnish with fresh cilantro.