Warm olive oil in a large Dutch oven or stock pot over medium heat. Add onions and cook until translucent, about 5 minutes.

Add mushrooms and sprinkle with 1/2 teaspoon of salt. Cook until they have released their liquid and most has evaporated, about 10 minutes.

Clear space in the middle of the pan and add garlic. Cook until fragrant, 30 to 60 seconds, then stir into the vegetables.

Add chicken stock, water, thyme, bay leaf, and remaining 1 1/2 teaspoons of salt. Increase heat to high and bring to a boil. Add chicken and let the soup return to a rapid simmer, then reduce heat to medium-low.

Cook until chicken is cooked through and pulls apart easily with a fork, about 10 to 15 minutes. Transfer chicken to a plate to cool.

Bring soup back to a rapid simmer. Break lasagna noodles into bite-sized pieces and add to soup. Stir in baby spinach and cook until noodles are al dente and spinach is wilted, about 8 to 10 minutes.

Shred the chicken into small pieces with two forks.

When noodles and spinach are done, add shredded chicken back to the soup and remove thyme stems and bay leaf. Stir in shredded Parmesan and milk, then return soup to a simmer. Taste the broth and add more salt or pepper if needed.

Remove from heat and ladle into bowls. Serve with a dollop or two of ricotta and a few cracks of fresh pepper.