Adjust oven rack to lower-middle position and heat oven to 300 degrees. Pat beef dry with paper towels and season with salt and pepper. Heat 1 tablespoon oil in large Dutch oven over medium-high heat until just smoking. Cook half of beef, turning occasionally, until well browned all over, about 8 minutes. Transfer to large bowl. Repeat with remaining oil and beef.
Pour off all but 1 tablespoon fat from pot. Add onions and ½ teaspoon salt and cook over medium heat until softened, about 8 minutes. Stir in chili powder, cumin, coriander, cayenne, and ¼ teaspoon pepper and cook until spices darken, about 2 minutes. Add garlic and cook until fragrant, about 30 seconds. Stir in tomato sauce and wine and bring to boil.
Add browned beef, along with any accumulated juices, to pot. Transfer pot to oven and cook, covered, until meat is fork-tender, 2 to 2½ hours. Transfer beef to large bowl. Strain sauce through fine-mesh strainer, discarding solids, and set aside. (You should have about 2 cups sauce.).
Increase oven temperature to 375 degrees. Spread ¾ cup sauce over bottom of 13- by 9-inch baking dish; set aside. When beef is cool enough to handle, shred into bite-sized pieces. Add 1 cup cheese and additional ¼ cup sauce and toss to combine.
Heat tortillas in the microwave for about 1 minute. Arrange warm tortillas on work surface. Place 1/3 cup beef mixture in center of each tortilla. Roll tightly and arrange, seam-side down, in prepared baking dish.
Pour remaining sauce evenly over enchiladas and sprinkle with remaining cheese. Cover with foil and bake until cheese is melted and enchiladas are heated through, 20 to 25 minutes. Serve.