Brown the Turkey: In a large pot, heat olive oil over medium-high heat. Add the ground turkey and cook, breaking it up with a spoon, until browned and cooked through, about 7-10 minutes. Remove the turkey from the pot and set aside.
Sauté the Aromatics: Reduce heat to medium and add the garlic, onion, and thyme to the pot. Cook for 3-4 minutes, or until the onions are softened and fragrant.
Add Vegetables and Herbs: Add the carrots, potatoes, and rosemary to the pot. Cook for an additional 3-4 minutes, or until the vegetables start to soften.
Simmer the Soup: Stir the cooked turkey, drained white beans, and chicken stock into the pot. Bring to a boil, then reduce heat to low, cover, and simmer for 45 minutes to 1 hour, or until the vegetables are tender.
Finish and Serve: Add the fresh spinach and cook for an additional minute, or until wilted. Season with salt and pepper to taste. Remove the thyme and rosemary sprigs before serving.