In a large pot over medium heat, add olive oil and butter. Once the butter is melted, add onion, carrots, garlic, salt (1/2 tsp), and pepper (1/2 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.
Notes
Note 1: Any small pasta shape will work, as long as it cooks in ~8 minutes. Avoid larger pasta shapes.Note 2: Use refrigerated, sandy-textured Parmesan cheese for the best flavor and melt. Do not use the shelf-stable type! It’s very salty and has less flavor. Storage: If storing leftovers, keep pasta separate from the soup to prevent the pasta from absorbing too much liquid and turning mushy. I use this spider strainer to remove pasta and store them separately from the broth and veggies. Reheat gently, adding a bit more broth or cream if it’s too thick.