Prepare the chicken liver stuffing by cooking chopped chicken livers in olive oil.

Combine cooked livers with breadcrumbs, chopped ham, garlic, parsley, sage, red pepper, nutmeg (or allspice), beaten egg, salt, and pepper.

Mix the stuffing ingredients until well combined.

Spoon the stuffing into the cavity of the chicken.

Truss the chicken to enclose the stuffing.

Place the stuffed chicken in a large stockpot.

Add 6 quarts of water and 1/2 teaspoon of salt to the pot.

Create a spice sachet by pressing cloves into an onion and placing it in cheesecloth with bay leaves, thyme, parsley, peppercorns, celery, and a cinnamon stick.

Tie the cheesecloth with kitchen twine to enclose the spices.

Add the spice sachet to the stockpot.

Cover the pot and bring to a boil over medium-high heat, skimming off any foam that rises to the surface.

Reduce heat to medium, uncover, and simmer until the broth gradually reduces, about 30 minutes.

Tie leek pieces in a bundle with kitchen twine.

Add the leek bundle, carrots, and turnips to the stockpot.

Add more water if necessary to just cover the chicken and vegetables.

Season with salt.

Continue simmering until the chicken and vegetables are very tender, about 1 hour.

Check for doneness by ensuring the chicken leg meat pulls away from the bones and the juices run clear when the chicken thigh is pierced with a fork.

Transfer the chicken to a cutting board and loosely cover to keep warm.

Transfer the vegetables to a large bowl using a slotted spoon; cut the twine from the leeks.

Return the pot to the stove over medium-high heat and bring to a boil.

Cook until the liquid has reduced by a third (approximately 2 1/2 quarts), about 15 to 25 minutes.

Strain the liquid into a medium saucepan, discard the cheesecloth packet, and season with salt.

Add vermicelli pasta to the saucepan and place over medium-high heat; bring to a boil, then reduce heat to a simmer.

Simmer until the pasta is just tender, about 2 minutes.

Garnish with parsley.

Remove the kitchen twine from the chicken.

Remove the stuffing from the cavity and transfer to a large serving platter.

Arrange the vegetables around the stuffing and place the chicken on top.

Garnish with fresh sage and serve with the pasta and sea salt.