Heat a heavy soup pot or Dutch oven over medium-high heat. Add olive oil and mushrooms and cook, while stirring occasionally, until mushrooms start to release their juices, approximately 6-7 minutes. Season with salt and pepper, to taste.

Add white parts of onion to pan and cook for 1-2 minutes, stirring once or twice.

Increase heat to high and add the Marsala wine. Cook until wine has reduced to 1/3 of its volume, approximately 4-5 minutes.

Add chicken stock and shredded chicken and bring to a boil. Reduce heat to just below medium. Simmer until heated through, approximately 4-5 minutes.

Remove from heat and ladle into individual soup bowls. Garnish with green parts of onion and serve immediately.