Cook rice according to package directions.
In a large Dutch oven or pot, heat about 2-3 tablespoons of olive oil to medium heat. Sauté the diced onions, carrots and celery until softened, about 10 minutes.
Add the minced garlic, thyme, dried oregano, and sauté for another 2 minutes until fragrant. Add the sliced mushrooms and cook for another 3 minutes.
Stir in the flour evenly over the vegetables, stirring to coat evenly for another 2 minutes to cook off any raw flour taste. Then, gradually pour in the 6 cups of chicken broth, stirring to dissolve the flour and break up any lumps. Bring to a boil, and then reduce to a simmer for about 10 minutes, half-covered. It will thicken as it heats up.
Stir in the cooked rice and cooked turkey meat. Season with salt and pepper to taste. Bring back to a boil and then simmer for another 5 minutes, or until heated through. If needed, add more broth until desired consistency.
Finish it with half-and-half until warm. Serve with bread or crackers. Enjoy!