Soak the dried chilies in warm water for 15-20 minutes until softened, then drain well.
Dry-roast cumin seeds, coriander seeds, peppercorns, cloves, cinnamon, and mustard seeds in a skillet over medium heat for 2-3 minutes until fragrant. Cool completely.
Blend the toasted spices with soaked chilies, garlic, ginger, turmeric, and vinegar until smooth, adding a tablespoon of water if needed to form a thick paste.
Coat chicken pieces thoroughly with two-thirds of the vindaloo paste and marinate for at least 30 minutes, or up to overnight for deeper flavor.
Heat oil in a Dutch oven over medium heat. Cook chopped onions with salt for 15-18 minutes until deeply golden brown and caramelized.
Stir in the reserved vindaloo paste and cook for 3-5 minutes until the oil separates from the masala, then add the marinated chicken and brown for 5-6 minutes.
Add water or broth and sugar, scraping up any browned bits from the pan. Cover and simmer for 25-30 minutes until chicken is tender. Uncover for the final 5-7 minutes to thicken the sauce.
Adjust seasoning with salt or extra vinegar if desired. Garnish with fresh cilantro and serve hot with rice or naan.