Boil the pasta in salted water until al dente. Drain and set aside.
In a skillet, melt butter over medium heat. Whisk in flour to form a roux and cook for about 1-2 minutes until lightly golden.
Add the garlic and sauté until fragrant. Stir in tomato paste and cook until the color deepens.
Pour in the chicken broth slowly, scraping up brown bits from the bottom of the pan.
Whisk in the heavy cream and reduce heat to medium-low. Stir occasionally until the sauce thickens.
Add sun-dried tomatoes, oregano, and red pepper flakes. Let everything simmer for a couple of minutes.
Fold in fresh basil and shredded chicken. Stir well to combine.
Lower the heat and add Parmesan cheese. Stir until it melts into the sauce.
Combine with the cooked pasta, tossing until evenly coated.
Serve hot, garnished with extra basil or Parmesan if desired.