Combine paprika, cumin, coriander, 1 1/2 tsp salt, garlic powder, 1/2 tsp pepper, oregano, and thyme in a small bowl and set aside. Pat the chicken completely dry with paper towels—this is crucial for achieving crispy skin. Prepare all vegetables: cut potatoes into 1-inch chunks, bias-cut carrots into 1/2-inch thick slices, slice the bell pepper, wedge the small onions, smash the garlic cloves, and halve the grape tomatoes. I like to keep the vegetables separate until mixing so I can control how evenly they're coated with oil.
Rub the dried chicken all over with 1/4 cup extra virgin olive oil, working it into all the crevices and under the skin if possible. Generously coat the chicken with the spice mixture from Step 1, pressing the spices gently so they adhere to the oiled skin. Let the seasoned chicken sit while you prepare the vegetable tray.
Spread the prepared potatoes, carrots, onions, garlic, mushrooms, tomatoes, bell pepper, and kalamata olives in a large roasting pan (approximately 9x13 inches or similar). Drizzle with 3 tbsp extra virgin olive oil, sprinkle with 3/4 tsp salt and 1/2 tsp pepper, then toss everything together until evenly coated. Arrange the vegetables so they create a bed in the center of the pan—this will cradle the chicken and allow juices to drip down.
Preheat your oven to 450°F. Place the seasoned chicken breast-side up on top of the vegetable bed in the roasting pan. Roast at 450°F for 15 minutes to develop a golden, crispy skin and jumpstart the cooking process. This high-heat start creates excellent browning and flavor development on both the chicken and vegetables.
After 15 minutes at 450°F, reduce the oven temperature to 350°F and continue roasting for 50-60 minutes until the chicken reaches an internal temperature of 165°F when checked with a meat thermometer in the thickest part of the thigh (without touching bone). The vegetables will finish cooking during this time, becoming tender and caramelized. I find that lowering the heat prevents the skin from burning while the inside cooks through evenly.
Remove the roasting pan from the oven and let the chicken rest for 10 minutes before carving—this allows the juices to redistribute throughout the meat, keeping it moist and tender. Drizzle the finished dish with fresh lemon juice from the 1/2 lemon. Slice the chicken and serve it on a platter surrounded by the roasted vegetables and pan juices.