Mix together the ground turkey, oregano, basil, garlic, fennel, crushed red pepper, and 1/2 tsp salt in a large bowl until well combined.
Heat 1 TBSP of the oil in a dutch oven or large pot over medium-high heat. When the oil is hot add the turkey mixture to the pot and cook while occasionally breaking up the turkey until browned, about 7 minutes. Transfer the cooked turkey to a plate and set aside.
Keep the pot over medium-high heat and add the remaining 1 TBSP of oil, the onion, and the carrot. cook, stirring often, for about 5 minutes.
Stir in the water and 1 tsp salt and use a wooden spoon or spatula to scrape the bottom of the pot to release any stuck on bits then bring to a boil.
When soup begins boiling add the potatoes and cooked turkey. Return to a boil then reduce the heat to medium-low and simmer until potatoes are tender, about 20 minutes.
Stir in the kale and cook until softened, about 5 minutes.
Stir in the heavy cream until thoroughly combined then simmer over medium-low heat until soup is heated through, about 5 more minutes.
Season the soup with additional salt & pepper to taste.