Ingredients

3 carrots, cut into thirds 

2 stalks celery, cut into thirds 

1 bulb fennel, cut into large chunks 

3 tablespoons fennel seeds, toasted 

1 teaspoon whole black peppercorns 

1 whole chicken (4 to 6 pounds) 

2 pounds chicken wings, necks, and backs 

3 quarts low-sodium canned chicken broth (two 48-ounce cans) 

2 quarts cold water 

Preparation

In a large stockpot, combine all ingredients. Cover, and bring to a boil over medium-high heat; reduce heat to a very gentle simmer. Cook, uncovered, 1 hour, checking occasionally to make sure the liquid is barely bubbling, and skim surface with a large metal spoon as needed.

Transfer whole chicken to a cutting board. Let cool slightly, and pull meat from the sides. (Reserve meat for another use; store in refrigerator up to 3 days, covered well with plastic wrap.)

Return chicken bones to pot. Place a smaller pot lid on surface of stock to keep ingredients submerged. Simmer until bones fall apart when poked, 2 1/2 to 4 hours. Skim surface as needed.

Prepare a large ice bath. Strain stock through a fine sieve into a large heat-proof bowl, discarding solids. Set bowl in ice bath, and let stock cool to room temperature, stirring frequently.

Transfer stock to airtight containers. Refrigerate at least 8 hours or overnight. With a large metal spoon, skim off and discard fat layer that has collected on the top. If storing, leave fat layer intact (it helps to seal in flavor).