Toast the chiles in a small dry saucepan over medium heat until pliable, 5 minutes. Remove from the heat. Add 1 cup water, cover and let soften, 5 minutes. Transfer to a blender and puree.
Heat the oil in a large pot over medium-high heat. Toss the meat with 2 teaspoons each salt and pepper. Brown the meat in batches, about 5 minutes; remove. Add more oil if the pot is dry. Add the onion and a pinch of salt. Cook until softened, 3 to 5 minutes. Stir in the garlic and cumin.
Add 3 cups water, the beef broth, chile puree, meat, tortilla and brown sugar; stir. Reduce the heat, partially cover and gently simmer, stirring occasionally, until the meat is very tender, 2 hours 15 minutes to 2 hours 45 minutes. If the chili is not thick enough, uncover, increase the heat and continue to simmer. Stir in the vinegar and season with salt and pepper.