Drain 3 tablespoons of oil from the sun-dried tomato jar into a large skillet with sides. Chop the sun-dried tomatoes and set aside.
Add the chicken to the skillet and toss with the sun-dried tomato oil, Italian seasoning, salt, and pepper. Set the skillet over medium-high heat. Sear the chicken on both sides until golden, 3-5 minutes per side. Add the butter, garlic, thyme, sage, and season with chili flakes. Cook until lightly golden, 2 minutes.
Mix in the pumpkin, tomato paste, and wine or broth. Bring to a boil, cook for 3-5 minutes, then add the cream, nutmeg, and sun-dried tomatoes. Simmer for 10 minutes until the sauce thickens. Sprinkle over both cheeses.
Serve the chicken topped with fresh basil and crusty bread for dipping.
