Prepare Chicken: Pat chicken pieces completely dry with paper towels. Season generously with salt and pepper on all sides. Let stand at room temperature for 30 minutes to allow seasoning to penetrate.
Brown the Chicken: Heat vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. When oil shimmers, carefully place chicken pieces skin-side down, ensuring not to overcrowd. Brown for 4-5 minutes per side until golden brown and crispy. Remove chicken to a plate and set aside.
Build Aromatic Base: Reduce heat to medium. Add diced onions, celery, and carrots to the same pot, utilizing the rendered chicken fat. Cook for 5-7 minutes, stirring occasionally, until vegetables begin to soften and caramelize lightly.
Add Aromatics: Add minced garlic and cook for 30 seconds until fragrant. Stir in tomato paste and cook for 1-2 minutes, stirring constantly to prevent burning.
Deglaze and Combine: Pour in white wine (if using) to deglaze the pot, scraping up any browned bits from the bottom with a wooden spoon. These fond bits add incredible flavor to the final dish.
Begin Stewing: Return browned chicken pieces to the pot, nestling them into the vegetable mixture. Add chicken broth, bay leaves, thyme, and paprika. The liquid should come about two-thirds up the chicken pieces.
Simmer Low and Slow: Bring mixture to a gentle simmer, then reduce heat to low. Cover and cook for 1.5-2 hours, checking occasionally to ensure liquid maintains a gentle simmer (not a rolling boil).
Add Potatoes: About 30 minutes before the end of cooking time, add cubed potatoes to the pot. Continue cooking until potatoes are tender and chicken reaches an internal temperature of 165°F.
Final Seasoning: Remove bay leaves and taste the cooking liquid. Adjust seasoning with salt and pepper as needed. If you prefer a thicker gravy, whisk cornstarch slurry into the simmering liquid and cook for 2-3 minutes until thickened.
Rest and Serve: Let stewed chicken rest for 10-15 minutes before serving. Garnish with fresh chopped parsley and serve with your favorite sides.