Heat 2 tablespoons sun-dried tomato oil in a large Dutch oven over medium heat.
Add chopped onion; cook, stirring occasionally, until softened, about 5 minutes.
Stir in ¼ cup sun-dried tomatoes, the minced garlic, 1½ teaspoons Italian seasoning, ½ teaspoon crushed red pepper and ¼ teaspoon salt.
Cook, stirring constantly, until the mixture is fragrant and the tomatoes have darkened slightly, about 2 minutes.
Stir in chopped kale; cook, stirring constantly, until just wilted, about 2 minutes.
Add 5 cups broth, the rinsed beans and ¼ cup basil; bring to a boil over medium heat.
Reduce heat to maintain a lively simmer; cook, uncovered, stirring occasionally, until the kale is tender, about 15 minutes.
Remove from heat.
Stir in ⅓ cup cream, 3 ounces cream cheese and ⅓ cup Parmesan.
Whisk until the cream cheese is melted and the mixture is fully combined.
Divide among 4 bowls.
Top each with 1 tablespoon Parmesan.
Garnish with additional basil, if desired.
