Place a vertical roaster in the oven and preheat the oven to 400 degrees F.

While the oven and pan are preheating, combine the onion, carrot, celery, garlic, and thyme in a mixing bowl with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Drizzle with 2 tablespoons of the olive oil and then toss thoroughly to combine. Set aside.

Rub the chicken well on all sides with the remaining 2 tablespoons of olive oil, then season well inside and out with the remaining 2 teaspoons of salt and remaining 3/4 teaspoon of pepper. Set aside.

Once the oven and roaster are preheated, carefully remove the vertical roaster from the oven using oven mitts and transfer to a heatproof surface. Spoon the seasoned vegetables into the outer well. Add the white wine to the inner well of the roaster, then carefully pour the chicken broth over the vegetables in the outer well; take care when adding liquids to the hot pan as it may splatter. Position the chicken over the inner well so that it sits securely upright. Return hot pan to the oven and allow to cook, undisturbed, until chicken is golden brown, skin is crispy, and an instant-read thermometer inserted into the deepest portion of the thigh registers 165 degrees F, 45 to 50 minutes. Remove from the oven and set aside to rest for at least 5 minutes before serving.

When ready to serve, transfer the chicken to a carving board and cut into pieces. Serve the chicken with the vegetables and drizzle with the pan juices.