Season the chicken on all sides with 2 teaspoons of the salt and black pepper to taste. Sprinkle the flour over the chicken and turn it to coat.
Heat the oil over medium-high heat in a 3 or 4-quart deep skillet or saute pan until it begins to shimmer. Add the chicken in 2 batches and sear until golden on both sides, about 5 minutes per side. Remove to a platter.
Add the onion and garlic to the pan and cook until softened and fragrant, about 3 minutes. Pour in the wine and let it bubble 1 minute. Add the stock or water and 1/4 teaspoon salt. Return the chicken to the pan and add the tomatoes. Put the herb sprigs on top of the chicken.
Cover the pan and turn the heat down to a very low simmer. Cook 30-35 minutes for boneless chicken and 60-75 minutes for bone-in pieces. The chicken meat should be tender and falling off the bone.
Cook the pasta in a large pot of salted water until al dente. Drain and transfer to a large serving bowl.
Pull the thyme sprigs out of the pan and discard. Using two forks, break the chicken in the pan into large chunks. If you cooked bone-in thighs, discard the bones and stir the meat to combine with the pan sauce. If you're using cream, stir it in.
Pour the chicken and the pan sauce over the pasta. Sprinkle with the cheese and additional thyme leaves and toss everything together. Enjoy!
Add a pinch of crushed red chili pepper along with the sun dried tomatoes.
Stir in a handful of baby spinach into the sauce when the chicken is cooked.
Tips:The best pan to use for this stovetop braised chicken is a 3 or 4-quart capacity deep skillet or heavy saute pan with a lid.Look for dried tomatoes that are plump, pliant and brightly colored, rather than hard brownish ones.