Heat the oven to 425 degrees. Pat the chicken dry with paper towels and place it in a large roasting pan.
In a small bowl, mix 2 tablespoons of the olive oil with the rosemary, thyme, salt, and pepper. Rub this mixture all over the chicken, including under the skin where possible. Stuff the garlic cloves inside the cavity.
In a large bowl, toss the carrots, potatoes, parsnips, and onion with the remaining tablespoon of olive oil. Arrange the vegetables around the chicken in the pan.
Roast for 60 to 75 minutes until the chicken reaches 165 degrees in the thickest part of the thigh and the vegetables are tender. Remove the pan from the oven and transfer the chicken and vegetables to a serving platter. Cover loosely with foil.
Place the roasting pan over medium heat on the stovetop. Sprinkle the flour over the drippings and whisk for 1 minute. Slowly pour in the chicken broth while whisking to remove lumps. Simmer for 3 to 4 minutes until the gravy thickens. Strain if desired and serve alongside the chicken and vegetables.