Preheat the oven to 350 degrees F.
Put the tomatillos, onion, serrano, yellow chile and 3/4 cup water in a medium, heavy saucepan. Bring to a boil over medium-high heat. Cover and boil until the tomatillos turn olive-green color, about 10 minutes. Transfer the tomatillos, onion and chiles to a blender. Add the garlic and cilantro and blend until smooth. Season with salt and pepper.
Heat the oil in a small skillet over medium-high heat. Fry the tortillas until golden but still pliable, about 10 seconds per side. Transfer to paper towels to drain.
Put the tortillas on a work surface. Divide the shredded chicken evenly among the tortillas, top with a little cheese and roll up each like a cigar. Spread 1/3 cup sauce in a 9 by 13-inch glass baking dish. Arrange the enchiladas, seam-side down, in one layer snugly inside the dish. Pour the remaining sauce over the enchiladas.
Drizzle with the Mexican crema and sprinkle the cheese all over. Bake until the cheese melts and starts to brown in spots, about 30 minutes. Serve immediately.