Pre-heat oven to 320f (160c)
Brown the chicken. Pat the chicken thighs dry and season well with salt and pepper. You can use two large frying pans at the same time, or work in two batches using one pan.
Heat 1 tablespoon olive oil per pan (or per batch) over medium-high heat. Brown the thighs for 3 minutes each side, starting skin-side down, until deeply golden. You don’t need to cook them through. Remove and set aside.
Cook the pancetta. Add the pancetta to a cold Dutch oven (or other ovenproof pot with a lid). Place over medium heat and cook for about 10 minutes, stirring occasionally, until golden and the fat has rendered.
Remove with a slotted spoon, leaving the rendered fat behind.
Cook the soffritto. Add the onion, carrot, celery and fennel seeds to the pot and cook gently for 15 minutes, stirring occasionally. If the pot seems dry, add a tablespoon of olive oil.
Add the garlic and ½ teaspoon each of salt and pepper in the last few minutes of cooking the soffritto.
Reduce the wine. Pour in the wine and let it reduce gently for 3-4 minutes.
Add the chicken stock and milk and mix well. Bring to a gentle simmer.
Return the pancetta to the pot then nestle the herb bundle in.
Place the chicken thighs and any accumulated juices in the pot. The liquid should cover most of them but the tops will poke out.
Cover with the lid and transfer to the oven. Cook for 75 minutes. You are looking for the meat to pull away very easily from the bone.
Mix the butter and flour. While the chicken is cooking, mash the softened butter and flour together with a fork until completely combined into a smooth paste. Set aside. This will be used to thicken the braising liquid at the end.
After 75 minutes, remove the chicken thighs and discard herb bundle. Remove the skin and shred the meat from the bones with two forks. Discard bones and skin.
Reduce the sauce. While you shred the chicken, place the pot over medium heat and bring the braising liquid to a steady simmer.
Use a spoon to skim any fat from the surface and around edges (see video below).
Add the flour and butter mixture to the simmering sauce and whisk in well. Simmer for 5-7 minutes, stirring regularly, until slightly thickened and glossy.
Finish the ragu. Stir in the lemon juice and zest, then return the shredded chicken to the pot. Simmer for 2-3 minutes until heated through. Taste and season as needed.