In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and cook until softened, about 3-4 minutes.
Add minced garlic and cook for an additional 1 minute, being careful not to burn the garlic.
Add the chicken pieces to the pot and cook until browned on all sides, about 5-7 minutes.
Pour in the Marsala wine and scrape the bottom of the pot to integrate any browned bits. Let it simmer for about 5 minutes until the wine reduces slightly.
Add the chicken broth, heavy cream, sliced mushrooms, dried thyme, salt, and pepper. Stir well to combine.
Bring the soup to a boil, then reduce the heat to a simmer.
Add the gnocchi to the pot and cook according to package instructions (about 2-4 minutes), until they float to the top.
Once the gnocchi is cooked, stir in the chopped parsley and adjust seasoning if necessary.
Serve hot, garnished with additional parsley if desired.