Preheat the oven to 350F degrees. Place a piece of parchment paper or foil on a sheet pan. Heat the olive oil in a large skillet over medium heat. Add the onion and celery and cook stirring occasionally, until the vegetables are soft, about 7 minutes. Set aside to cool slightly. In a large bowl combine the beef, turkey, parsley, thyme, eggs, milk, salt, and pepper. Add the onion mixture and the oats and combine with clean hands until mixed well. Form into 1 long or 2 smaller rectangle loafs. Bake 50 minutes, or until a thermometer inserted in the middle reads 160 degrees. Remove from the oven and rest for 10 minutes. Meanwhile, when the meatloaf is almost ready, combine the cold beef broth, thyme and flour in a small saucepan and whisk well over medium heat until it comes to a boil, then simmer over medium-low heat until it thickens, stirring occasionally about 5 minutes. Pour the pan drippings, if any into the gravy and continue to whisk another minute. Adjust salt and pepper to taste, as needed, then discard thyme. Slice the loaf into 24 slices (if making 1, or 12 slices each if making this into 2 loaves) and serve hot with the gravy. Garnish with parsley if desired.