Cook rice according to package directions. It should take about 45 minutes if using wild rice blend.
Heat a large Dutch oven to medium heat and add 2 tablespoons olive oil and 1 tablespoon unsalted butter. Sauté garlic, onion, carrots and celery until softened, about 5-8 minutes. Add thyme, dried oregano, and mushrooms and cook for another minute. Stir in flour and cook for about 3-4 minutes.
Add broth little by little, 2 cups at a time, stirring to make sure the liquid and the base are combined evenly. I added 6 cups, but if you prefer, add more until desired consistency. Keep in mind that it will thicken up as it boils since we added flour.
Stir in 3 cups cooked rice and cooked turkey. Season with salt and pepper to taste. Bring to a boil and then bring the heat back down to a simmer. Cook for 15 minutes, covered.
Stir in half-and-half, and simmer for another 5 minutes.
Serve with bread or crackers. Enjoy!