Heat the olive oil in a soup pot over medium-high heat. Add the mushrooms, 1 teaspoon salt, and ½ teaspoon pepper. Cook until the mushrooms release their juices and start to brown, about 8 minutes. Add the white parts of the green onions and cook for another minute. Add the Marsala wine, increase heat to high, and cook until most of the wine has evaporated. Add the chicken and chicken stock. Bring to a boil, then lower the heat and simmer until heated through, about 5 minutes. Garnish with the green parts of the green onions and serve immediately.