In a large bowl, combine the chicken pieces with white vinegar, minced ginger, minced garlic, ground turmeric, ground cumin, ground coriander, ground cinnamon, paprika, cayenne pepper, and salt. Mix well to coat the chicken evenly. Cover and refrigerate for at least 1 hour, preferably overnight for best results.
Heat the vegetable oil in a large skillet or pot over medium heat. Add the finely chopped onion and cook until golden brown, about 5-7 minutes.
Add the mustard seeds and dried red chilies (if using) to the skillet. Cook for another minute until the mustard seeds start to pop.
Add the marinated chicken to the skillet and cook until the chicken is browned on all sides, about 5-7 minutes.
Stir in the diced tomatoes, tomato paste, and chicken broth. Bring to a simmer.
Add the brown sugar and stir to combine. Reduce the heat to low and let the vindaloo simmer for 20-25 minutes, until the chicken is cooked through and the sauce has thickened. Adjust the seasoning with salt if needed.
Garnish with chopped fresh parsley or cilantro and serve hot with steamed rice or naan bread.