Preheat the oven to 425 degrees F and place a rack in the lower third position of your oven. Spread the onions and carrots evenly in your roasting pan.

Take the chicken out of the refrigerator and allow it to sit at room temperature for about 2 hours. If the chicken is cold, it will be difficult to cook it evenly. Remove the chicken giblets and rinse the chicken inside and out. Pat the chicken thoroughly dry with paper towels, and season the cavity liberally with salt and pepper. Then combine the melted butter and olive oil with an additional 2 ½ teaspoons of salt and 1/2 teaspoon pepper. Rub this mixture all over the outside of the chicken, as well as under the skin where you can get it.

Put the thyme inside the cavity, along with the lemon and garlic halves. Tie the legs together with kitchen string, and place the chicken on top of the bed of carrots and onions, breast-side up.

Roast for 75-85 minutes, or until the juices run clear when you cut between the leg and thigh.

Remove the chicken and vegetables to a platter and cover with aluminum foil for about 20 minutes. Slice the chicken, and serve it with the vegetables. Reserve the pan drippings for the stock.

Once you’re done eating the chicken, remove the lemon halves, thyme and garlic that you roasted the chicken with. Add the chicken carcass to a stockpot. You can also add any leftover roasted vegetables you may have.

Take half of your warm water and pour it into your roasting pan. Use a spoon to lift up all the bits from the bottom of the pan, and pour the liquid from the pan into your stockpot.

Add the additional 6 cups water, carrots, celery, onion, garlic, peppercorns, and bay leaves. Bring to a boil, and then reduce the heat to low. Cover. Allow the stock to simmer for about 6-8 hours, periodically skimming any foam off the surface.

Strain the stock into containers, and freeze, or use the stock for whatever soup or other application you like. You could even serve the stock in bowls or mugs with a pinch of salt for a warming winter tonic!