Heat a cast-iron skillet over high heat. Place chiles in pan; flatten with a spatula. Cook 5 seconds on each side or until blackened. Combine toasted chiles and 2 cups boiling water in a bowl; let stand 20 minutes or until soft. Place the chile mixture in a blender or food processor; process until smooth.
Heat a Dutch oven over medium-high heat. Add chopped onion, chopped chorizo, and minced garlic; cook 5 minutes or until browned, stirring frequently. Add the pureed chile mixture, Swiss chard, and next 5 ingredients (through tomatoes); bring to a boil. Reduce heat, and simmer 30 minutes. Warm tortillas according to package directions. Serve soup with tortillas; sprinkle with queso fresco.