Remove any tough outer layers from the leek. Trim the bottom, then cut it in half crosswise to separate the dark green top from the lighter bottom.

Thoroughly rinse both halves. Set aside the dark green parts of the leek. Thinly slice the white and light green parts into rounds. You may wish to place the sliced rounds in a fine-mesh sieve and rinse again under running water to remove any stubborn grit or dirt.

Carefully remove the chicken from the pot and transfer it to a large bowl. Remove the head of garlic and transfer it to a small bowl.

Bring the broth to a rapid simmer over medium heat and cook uncovered for 20 to 30 minutes to reduce and concentrate the flavor.

Pour the broth into a large bowl through a fine-mesh sieve. You should have about 8 to 10 cups of broth. Discard the solids. Wipe out the pot and return it to the stove.

Once the chicken is cool enough to handle, remove the skin and pick the meat from the bones. Carefully shred or chop the chicken into bite-sized pieces. Reserve the skin and carcass for stock, if desired.

Carefully squeeze the garlic cloves from their skins and mash them into a paste. Set aside.

Heat 1 tablespoon extra virgin olive oil in the soup pot over medium heat. Add the sliced carrots, diced onion, and the sliced white and light green parts of the leek. Sauté for 6 to 8 minutes until softened. Season with salt and pepper.

Add the garlic paste and stir to coat. Cook for 1 minute until fragrant.

Rinse 1 cup of white rice under cold water. Add to the pot and toss to coat. Cook for 1 minute.

Add the prepared chicken broth and shredded chicken. Bring to a boil. Reduce the heat to low and simmer, uncovered, for 30 to 40 minutes until the rice is tender and the broth has thickened. Taste and add salt and pepper as needed.

Combine the shredded cheddar cheese in a bowl with 1 tablespoon of cornstarch. Toss to coat. Stir into the soup until fully melted and smooth. Taste and season. Stir in the parsley and lemon juice and simmer for 5 minutes. Turn off the heat.

Ladle the soup into bowls. Finish with more shredded cheddar cheese and a pinch of minced parsley if desired. Enjoy!