Texas-Style Chili

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3 dried New Mexico chiles, stemmed and seeded

2 dried pasilla chiles, stemmed and seeded

2 dried guajillo chiles, stemmed and seeded

2 tablespoons vegetable oil, plus more if needed

2 1/2 pounds cubed beef stew meat (1- to 1 1/2-inch pieces) 

Kosher salt and freshly ground pepper

1 onion, chopped 

3 cloves garlic, minced 

2 teaspoons ground cumin

2 cups low-sodium beef broth

1 corn tortilla, torn 

2 tablespoons packed brown sugar

1 tablespoon apple cider vinegar