Heat olive oil in an ovenproof skillet cast iron skillet over medium-high heat.
Season chicken breasts with 1/2 teaspoon salt and pepper.
Add chicken to skillet and cook until golden, about 5 minutes. Turn and cook on the other side for another 5 minutes. Remove chicken from the pan and set aside.
In the same skillet, add tomato paste, garlic, and fennel seeds and cook until just fragrant, about 1 minute.
Add crushed tomatoes and red pepper flakes and bring to a simmer, allow to cook for 3 minutes.
Stir in heavy cream, ¼ cup parmesan cheese and kale, stirring until kale is just wilted, about 3 minutes.
Season with remaining ½ teaspoon salt and add chicken back into the skillet. Allow to cook for 5 more minutes or until the internal temperature of the chicken breasts reaches 165°F with an instant read thermometer.
Serve topped with fresh basil and remaining cheese.