Begin by preparing all the ingredients: dice the onion, mince the garlic, slice the carrots and celery, and cube the red potatoes into 1-inch pieces.

In a Dutch oven or a large pot with a capacity of at least 6 quarts, heat the olive oil over medium heat. Add the diced onion and minced garlic to the hot oil. Sauté until the onion becomes golden brown and releases a fragrant aroma.

Incorporate the sliced carrots and celery into the pot. Sauté for one minute to slightly soften the vegetables. Add the chicken or turkey broth, drained diced tomatoes, cubed potatoes, fresh thyme sprigs, and bay leaf. Increase the heat to bring the mixture to a boil, then reduce to medium-low heat. Allow the stew to simmer for approximately 10 minutes, or until the potatoes are tender when pierced with a fork.

Add the diced cooked turkey to the stew. Stir thoroughly to ensure the turkey is evenly distributed throughout the mixture.

Remove one cup of broth from the pot and place it into a separate bowl. Gradually add the all-purpose flour to the broth, whisking continuously until the flour is mostly dissolved and forms a smooth slurry. Pour this slurry back into the stew, stirring well to combine.

Increase the heat to medium-high and bring the stew back to a gentle boil. Continue to cook for a few minutes, allowing the stew to thicken to your desired consistency. Season with salt and black pepper according to your taste preferences.

Once the stew has thickened, remove the pot from the heat. Discard the thyme sprigs and bay leaf. Garnish with chopped fresh parsley if desired. Ladle the hot stew into bowls and serve immediately.