Season the chicken with ½ teaspoon of the salt, ensuring even coverage. In a large skillet, heat the olive oil over medium-high heat until shimmering. Add the chicken breasts and sear until golden brown, about 5 minutes on each side. Once browned, transfer the chicken to a plate and set aside.

In the same skillet, add the tomato paste, minced garlic, fennel seeds, and crushed red pepper flakes. Stir continuously for approximately 1 minute, or until the mixture becomes fragrant. Pour in the crushed tomatoes, stirring as it reaches a gentle simmer. Allow the sauce to cook for about 3 minutes before adding the heavy cream, ¼ cup of Parmesan cheese, and kale. Cook, stirring occasionally, until the kale wilts, roughly 3 minutes. Season with the remaining ½ teaspoon of salt.

Return the chicken to the skillet, nestling it into the sauce. Continue cooking until the internal temperature of the chicken reads 165°F on an instant-read thermometer, around 5 minutes. Sprinkle with the thinly sliced basil and the remaining Parmesan cheese before serving.