Start by heating the olive oil in a large pot over medium heat. Add the Italian chicken or turkey sausage to the pot, breaking it up with a wooden spoon. Cook until browned and cooked through, about 5-7 minutes. Once cooked, remove the sausage from the pot and set aside.
In the same pot, add the chopped onion and sliced carrot. Sauté for about 5 minutes until the onion becomes translucent. Add the chopped garlic and cook for another minute, stirring frequently to avoid burning.
Pour in the reduced-sodium chicken broth and water. Stir well to combine, then add the diced red potatoes and dried red pepper flakes. Bring the mixture to a boil.
Once boiling, reduce the heat to low and cover the pot. Let the soup simmer for about 15-20 minutes, or until the potatoes are tender when pierced with a fork.
After the potatoes are cooked, stir in the shredded kale and return the cooked sausage to the pot. Allow the soup to simmer for an additional 5 minutes, until the kale is wilted and tender.
At this point, add fresh ground pepper and kosher salt to taste. Adjust these seasonings according to your preference to ensure a delicious balance of flavors.