Dice bacon and cook in a large cast-iron pot (or Dutch oven) over medium heat until browned and fat is rendered. Use a slotted spoon to remove bacon to a paper towel–lined plate, leaving the fat in the pot.
While bacon cooks, pat chicken dry with paper towels. Season lightly with salt and pepper (about 1/2 tsp each). Increase heat to high. Add chicken, skin side down, and sear until golden, about 4-5 minutes per side or until it releases easily from the pan. Transfer chicken to a bowl, cover with foil, and set aside.
Reduce heat to medium-high. Add carrots, celery, and onion to the pot. Cook, stirring often, until beginning to soften, about 3 minutes. Stir in tomato paste and garlic, cooking for 30 seconds.
Increase heat to high. Add 1 cup chicken broth, 1 cup wine (or 1 cup additional broth), Worcestershire sauce, and bay leaves. Bring to a rapid simmer and cook, stirring occasionally, until reduced to about 1/3 cup (10–15 minutes).
Add butter to the pot and stir until melted. Sprinkle flour over the vegetables and stir until smooth, about 1 minute. Gradually whisk in the remaining 3 cups of chicken broth, then add thyme, sage, and paprika. Stir until smooth and combined.
Add potatoes and mix through. Return chicken (and any juices) to the pot, pressing pieces under the liquid as much as possible. Simmer, stirring occasionally and scraping the bottom, until the chicken registers 165°F on a thermometer, about 20 minutes.
Remove chicken and set aside to cool slightly. Continue simmering the stew over low heat until the potatoes are fully tender. Remove and discard the chicken skin, then shred or chop the meat. Return chicken to the pot along with the remaining 1/4 cup wine (or 1–3 tablespoons white wine vinegar, to taste) and the cooked bacon. Stir well. Season to taste with additional salt and pepper (I usually add another 1/2 teaspoon each). Remove and discard bay leaves.
Ladle stew into shallow bowls, garnish with parsley if desired, and serve with warm crusty bread.
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Notes
Note 1: Use 4–6 bone-in, skin-on chicken thighs. The bones add richness and keep the meat juicy while cooking.Storage: Refrigerate leftovers in a covered container for up to 5 days. Freeze for up to 3 months in an airtight container. Note that thawed potatoes may become slightly soft.