Place flour in a shallow bowl. Season the chicken with ½ teaspoon salt and ¼ teaspoon pepper then dredge in flour.
Heat 2 tablespoons oil in a Dutch oven over medium-high heat until shimmering. Add chicken to the pan and cook until golden brown, about 2 to 3 minutes per side. Transfer to a plate.
Reduce the heat to medium and add the remaining 1 tablespoon oil to the pan along with the onion. Cook, stirring frequently until softened, about 3 minutes. Stir in the garlic and cook until fragrant, about 1 minute. Add the tomato paste and cook, stirring often, for 3 minutes. Add sun-dried tomatoes, Aleppo pepper, oregano and broth and stir to combine. Return chicken to the pot, reduce heat to medium-low, cover partially with a lid and simmer, stirring occasionally, until chili thickens, about 30 minutes.
Remove lid and transfer chicken to a cutting board. Chop into bite size pieces and return to the pot along with the kale, beans, heavy cream, ¼ cup Parmesan cheese, ½ teaspoon salt, and ¼ teaspoon pepper. Simmer 5 minutes then portion into bowls and serve garnished with remaining cheese.
