Place the chicken in a stockpot. Add the carrots, onion, garlic, thyme, bay leaves, parsley, and black peppercorns on top—season liberally with salt. Add enough water to cover the chicken by 1 inch.
Bring to a boil and then reduce heat and simmer for 3–4 hours, skimming off any foam or scum that floats to the top.
Cool the chicken:
Remove the chicken from the pot and set it aside to cool.
Hard simmer the broth:
Bring the broth to a hard simmer (just below boiling) for 30 minutes or until it reduces slightly and takes on a dark golden color.
Strain the broth:
Strain the broth through a fine-mesh sieve into a large heatproof bowl. Discard solids. Wipe out the stockpot and return it to the stovetop.
Start the tortellini soup:
Heat the oil in the stockpot over medium heat. Once hot, add the onion, celery, and carrots and cook them for 7–8 minutes until they soften—season with salt and pepper.
Bloom the spices:
Melt the butter into the pot. Once bubbly, add the dry thyme and a pinch of crushed red pepper to taste.
Simmer the soup:
Add the cooked chicken to the pot along with the homemade chicken stock. If needed, add a cup or two of water. You should have about 8 cups of liquid in the pot. Bring the soup to a boil and then reduce heat and simmer for 20 minutes. Taste and season the broth to your preferences.
Finish the soup:
Add the escarole and lemon juice to the soup. Simmer an additional 10 minutes.
Cook the tortellini:
Meanwhile, bring a large pot of salted water to a boil. Add the tortellini and cook until al dente. Drain and divide the tortellini between bowls.
To serve:
Ladle the hot chicken soup over the tortellini. Serve with freshly grated parmesan cheese and minced parsley. Enjoy!