Heat a large pot over medium-high heat and then add oil. Stir in onions and garlic and cook until translucent.
Add chicken and cook chicken for about 2 minutes. Add salt, pepper, thyme, oregano, worcestershire sauce, and mushrooms. Stir and cook until mushrooms become soft.
Whisk flour/cornstarch into the cream (half & half or milk) until fully incorporated. Then add chicken broth and cream into the soup. Stir together with chicken and bring to boil, then immediately lower heat to a simmer.
Simmer soup for 10-15 minutes, or until the chicken is cooked, soup is thick and the flavors are combined. Add additional salt to taste.