Place the chicken in a large pot and cover with water. Add the onion and 2 teaspoons salt. Bring to a boil. Reduce heat and simmer, uncovered, for 1 hour. Remove foam and scum as it floats to the top of the broth while the chicken cooks.
Remove the chicken from the pot and transfer to a bowl. Return the broth to a low boil over medium heat. Simmer for 10–15 minutes or until the broth reduces and darkens a bit in color. You should be left with about 5–6 cups of broth.
Strain the broth through a fine-mesh sieve and discard the spent onion. Wipe out the pot and return it to the stovetop.
Prepare the chicken:
Once the chicken is cool enough to handle, carefully pick the meat from the bones and shred it with two forks or your fingers.
Discard the bones and skin. You can also dice the cooked skin and air-fry or pan-fry it to make a crunchy garnish for the soup if you like.
Cook the mushrooms:
Turn the heat on the pot to medium. Add the mushrooms and cook, turning occasionally, for 8–10 minutes. The mushrooms will release water, and that water will evaporate.
Once the water evaporates and the mushrooms begin to “squeak” in the pot, add 1 tablespoon olive oil and cook for 2 minutes until golden brown. Season with a pinch of salt.
Sauté the aromatics:
Add the onion, celery, and carrots to the mushrooms and cook for 5–7 minutes. Season with salt, pepper, thyme, paprika, and crushed red pepper to taste. Add the garlic and cook for 1 minute until fragrant.
Simmer the soup:
Deglaze the pot with 1 cup of white wine or water. Stir well to lift up anything stuck to the bottom of the pot. Bring to a boil for 5 minutes.
Pour in the prepared broth and bring to a boil. Stir in the chicken. Reduce heat and simmer, uncovered, for 20 minutes. Taste and season with salt and pepper.
Cook the rice:
Return the soup to a boil. Stir in the rice and reduce heat to low. Simmer for 20 minutes or until the rice is tender. Add another cup or two of water if the rice absorbs too much liquid. Taste and adjust the seasonings as needed.
Finish the soup:
Add the lemon juice and spinach. Simmer for 5 minutes. Turn off the heat.
To serve:
Ladle the soup into bowls. Serve with more lemon or the crispy chicken skin. Enjoy!