Toast chiles in dry skillet over medium about 2 minutes until fragrant; transfer to bowl and cover with 2 cups hot broth. Soak 15 minutes until softened.
Blend chiles, soaking liquid, garlic, cumin, oregano, and remaining 1 cup broth completely smooth; strain through fine-mesh sieve and salt to taste.
Pour sauce into wide shallow bowl; heat oil in large skillet over medium-high.
Quickly fry tortillas about 10 seconds per side just to soften; immediately dip in warm sauce to coat both sides.
Fold each in half like taco; fill with chicken and arrange slightly overlapping on plates.
Spoon extra sauce over; top with queso fresco, onion, crema drizzle, and cilantro. Serve immediately.