Brown the Sausage: Heat olive oil in a large pot over medium heat. Add the Italian sausage, breaking it up with a wooden spoon as it cooks. Continue cooking until the sausage is thoroughly browned and no longer pink, about 5-7 minutes. This step builds the foundational flavor for the entire soup.
Sauté Aromatics: Add the chopped onion and minced garlic to the pot with the browned sausage. Cook until the onion becomes translucent and softened, and the garlic is fragrant but not burned, approximately 3-4 minutes. Stir occasionally to prevent sticking.
Combine All Ingredients: Stir in the chicken broth, diced tomatoes with their juice, chopped kale, drained and rinsed cannellini beans, dried thyme, salt, and pepper. Bring the mixture to a boil, stirring occasionally to combine all flavors.
Simmer: Reduce the heat to low and allow the soup to simmer uncovered for 20-25 minutes. This gives time for the kale to become tender and for all the flavors to meld together beautifully. The soup will slightly reduce and intensify in flavor during this time.
Serve: Ladle the hot soup into bowls and serve immediately. The soup can be garnished with grated Parmesan cheese or a drizzle of olive oil if desired.