Season chicken with ½ teaspoon salt. Cook in olive oil until browned, about 5 minutes per side. Remove and set aside.
Add tomato paste, garlic, fennel seeds, and red pepper flakes to the skillet; cook until fragrant, about 1 minute. Add crushed tomatoes and simmer for 3 minutes.
Stir in heavy cream, pepper, Parmesan, and kale; cook until kale wilts, about 3 minutes. Return chicken and cook until internal temperature reaches 165°F, about 5 minutes.
Top with basil and Parmesan, then serve.
Notes
Use fresh basil for the best flavor and ensure chicken reaches 165°F for safety.