SAUCE: In a dry, deep skillet (preferably cast-iron) set over high heat, toast dried ancho, guajillo, pasilla, and costeña chiles, turning occasionally, until fragrant. Remove from heat, and cover with water. Add lid and let sit until softened, about 30 minutes. Remove stems and seeds, and purée with chiles in adobo, tomatoes, chicken broth, and salt until smooth. Set aside.

CHILAQUILES: Preheat oven to 375°F. Brush tortilla strips with olive oil. Arrange in a single layer on a baking sheet lined with parchment paper, sprinkle lightly with salt, and bake until crispy, 10 to 15 minutes.

In a skillet over medium heat, warm 1 tablespoon olive oil and sauté shallot until translucent. Add pasta and sauté 2 to 3 minutes. To assemble, spread a thin layer of sauce on bottom of a 2-quart rectangular casserole dish. Layer chicken, fideo, half the sauce, habanero or salsa Jack cheese, and queso fresco (reserve 1 cup for topping), ending with remaining sauce. (Note: Extra sauce is great on scrambled eggs.)

Bake casserole 20 minutes. Remove from oven, and top with tortilla strips and reserved queso fresco. Bake 5 minutes more, then broil 1 to 2 minutes until cheese is bubbly. Serve topped with cilantro, jalapeño, and, if desired, a soft fried egg.