In a large pot over medium heat, add olive oil and butter. Once the butter is melted, add onion, carrots, garlic, salt (½ tsp), and pepper (½ tsp). Sauté for 7–9 minutes, until tender.
Sprinkle flour on top and cook for 1 more minute, stirring constantly.
Slowly whisk in 1 cup of broth to form a slurry. Gradually add the rest of the broth, whisking and scraping the bottom of the pot.
Bring to a boil, then add pasta. Cook according to package directions, minus 1 minute. Stir occasionally to prevent sticking.
Reduce heat to low. Stir in cream, kale, and sun-dried tomatoes. Gradually add Parmesan (a few tablespoons at a time) and stir until melted.
Add chicken and stir well. Season with additional salt to taste. For a thinner soup, add more broth.
Ladle into bowls and serve hot with hearty buttered bread. Top with red pepper flakes for a little heat, if desired.
