In a large pot or Dutch oven, heat the olive oil over medium heat.
Add the Italian sausage, breaking it apart with a wooden spoon. Cook until browned, about 5-7 minutes.
Add the diced onion and sauté for another 3-4 minutes until softened.
Stir in the minced garlic and cook for an additional minute until fragrant.
Pour in the chicken broth and add the diced tomatoes (with juice), carrots, thyme, and red pepper flakes (if using). Bring the mixture to a boil.
Once boiling, reduce the heat to low and let the soup simmer for about 15 minutes.
Add the kale and pasta to the pot. Continue to simmer for another 10-12 minutes or until the pasta is cooked and the kale is tender.
Season with salt and pepper to taste.
Serve hot, garnished with grated Parmesan cheese if desired.