Heat olive oil in a large stockpot or Dutch oven over medium heat. Add Italian sausage and cook until browned, about 3-5 minutes, making sure to crumble the sausage as it cooks; drain excess fat.
Stir in garlic, onion and Italian seasoning. Cook, stirring frequently, until onions have become translucent, about 2-3 minutes; season with salt and pepper, to taste.
Whisk in flour until lightly browned, about 1 minute.
Gradually whisk in chicken stock and tomato sauce. Bring to a boil; reduce heat and simmer, stirring occasionally, until reduced and slightly thickened, about 10 minutes.
Stir in tortellini; cover and cook until tender, about 5-7 minutes.
Stir in kale until wilted, about 1-2 minutes. Stir in heavy cream and basil until heated through, about 1 minute; season with salt and pepper, to taste.
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