Pat chicken thighs on all sides with a paper towel until dry. Using a paring knife or sharp kitchen scissors, remove excess fat from meat. Season on both sides with salt and pepper.
In a Dutch oven, heat olive oil over medium. Add chicken thighs, cooking undisturbed for 4-5 minutes, until slightly browned. Flip and cook on alternate side. When browned, remove from pot and reserve on plate. Don’t worry if the chicken isn’t fully cooked through, it will braise in the sauce.
In the same pot, heat remaining olive oil on medium-low. Stir in carrots, celery, garlic, and Italian seasoning, plus chili flakes, if desired. Once fragrant, about five minutes, stir in tomato paste to carmelize. Once well incorporated, deglaze the pot with wine, scraping up any browned chicken bits. Stir in tomato puree, Parmesan rind (if using) and return chicken and any juices to the pot. Season with salt and pepper, as desired. Stir.
Cover the pot with just a small opening for steam to escape, lower heat to low, and let simmer for 1-2 hours, stirring every so often.
Remove chicken thighs from pot and return to resting plate. Using two forks, shred the meat finely. Return the shredded meat to the pot, stir and reduce heat to low.
Cook pasta according to al dente package directions, strain and reserve 1 cup of cooking liquid. Add pasta to chicken ragu, stirring in a splash of pasta water to help the sauce stick. Add more sauce if necessary to loosen the sauce. Serve with parmesan cheese.
Sauce can be cooked 2-3 days in advance and reheated with pasta and its cooking water for a fresh meal. The sauce also stays well in the freezer for 3-4 months and can be served with polenta, egg noodles or a variety of starches.