Heat 1 tablespoon of olive oil in your soup pot over medium heat. Add the diced onion, celery, and carrot. Cook for about 5 minutes, stirring occasionally, until the vegetables are softened and the onions are translucent.
Toss in the sliced white mushrooms and minced garlic. Cook for another 5 minutes, stirring frequently, until the mushrooms release their moisture and begin to brown slightly.
Sprinkle in the salt, pepper, oregano, and thyme. Stir well to coat the vegetables evenly. Add the diced russet potato and the bay leaf, stirring to combine everything.
Pour 4 cups of low-sodium chicken stock into the pot. Bring the mixture to a boil, then reduce the heat and let it simmer for 10-12 minutes, or until the potatoes are tender when pierced with a fork.
Stir in the diced or shredded cooked chicken breast. Allow it to warm through for 2-3 minutes. Finally, pour in the half & half, stirring to create a creamy, luscious broth. Remove the bay leaf before serving.
Give your soup a taste and adjust seasoning as needed with additional salt or pepper. Ladle into bowls and enjoy immediately, or save for later.