In a pot, heat the oil over medium heat. Add the turkey, onion and garlic; saute while breaking up the turkey into smaller pieces.
Stir in the broth, tomatoes, thyme, and season with salt and pepper. Cover with a lid and bring to a simmer, stirring occasionally, for about 20 minutes.
Taste and adjust the seasoning with salt as needed. Stir in the tomato paste and cream and continue to simmer until the soup starts to thicken. (Add more tomato paste if needed a little at a time to thicken to your desired consistency).
Remove the thyme sprigs.
Serve with crackers. Drizzle the top of the soup with olive oil, season with salt and pepper. Garnish with parsley and red pepper flakes.