Begin by heating a splash of olive oil or a knob of butter in a large pot over medium heat. Add the chopped onion and celery, cooking until they become soft and translucent. This should take about 5 minutes. Stir occasionally to prevent the vegetables from sticking to the bottom of the pot.
Add the mushrooms to the pot with the onions and celery. Cook them until they turn golden brown, stirring often to ensure even cooking across all the mushrooms. This typically takes about 5-7 minutes.
Once the mushrooms are cooked, add the thyme and minced garlic to the pot. Cook for about 1-2 minutes, stirring constantly, until the garlic becomes fragrant. Be careful not to let the garlic burn as it can turn bitter.
Pour in the chicken or vegetable stock along with the cream. Stir the mixture well, then bring it to a gentle simmer. Let it cook for about 5 minutes, allowing the flavors to meld together.
Add the cooked, shredded chicken and fresh spinach to the simmering pot. Continue to simmer for another 5 minutes, until the spinach wilts and the chicken is heated through.
Season the soup with salt and pepper to taste. Add a splash of lemon juice for brightness and adjust the seasoning if necessary. Serve the soup hot, accompanied by your favorite bread for dipping.