In a large Dutch oven or heavy-bottomed pot, heat the olive oil over medium-high heat. Season the chicken cubes with 1/2 tsp salt and 1/4 tsp black pepper. Add the chicken to the pot and cook until browned on all sides and cooked through, about 5-7 minutes. Remove the chicken from the pot and set aside.

Reduce heat to medium. Add butter to the same pot. Once melted, add the diced onion, celery, and carrots. Cook, stirring occasionally, until softened, about 8-10 minutes.

Stir in the sliced mushrooms and cook until they release their liquid and start to brown, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the flour over the vegetables and stir continuously for 1-2 minutes to cook out the raw flour taste, creating a roux.

Gradually whisk in the chicken broth, a cup at a time, ensuring no lumps form. Bring the soup to a simmer, then reduce heat to low, cover, and let it gently simmer for 10 minutes to allow the flavors to meld and the soup to thicken slightly. Stir in the dried thyme.

Stir in the heavy cream and return the cooked chicken to the pot. Heat through for 2-3 minutes, but do not bring to a rolling boil after adding cream to prevent curdling.

Taste and adjust seasoning with additional salt and pepper as needed. Stir in the fresh chopped parsley just before serving. Serve hot.