In a food processor, combine the onion, garlic, tomato, quince, chestnuts, cilantro, dill, salt, pepper, and chiles. Pulse until well mixed, but ensure the pieces still have their shape. Do not overprocess. Add the meat and rice and mix again until well integrated.
If using bottled cabbage leaves, rinse and dry each leaf. If using fresh cabbage, separate the leaves and boil in lightly salted water until tender but still firm. Drain and pat dry. As a third alternative, freeze the whole head of cabbage, then let it thaw to make the leaves pliable enough to roll. If desired, cut the extremely large leaves into more manageable sections. (I like to use leaves that are 4 to 6 inches long for appetizer-size rolls and leaves that are 6 to 8 inches long for larger dinner-size rolls.)
Depending on the size of the leaf, place 2 to 3 tablespoons of filling about 2 inches from one edge and then roll the leave lengthwise, tucking in the top and bottom as you roll to make compact squarish rolls.
For the broth: Melt the butter in a wide pot or saute pan and add the vinegar, sugar and about half of the broth. Place rolls in the pan in one layer and pour over the remaining broth. Cover with a lid and cook over low heat until the meat is cooked through, 30 to 40 minutes.
Serve with boiled potatoes for a light meal or as part of a larger multicourse feast.