Heat oil in a 3 1/2-quart flameproof nonreactive shallow casserole or deep skillet to 375 degrees F. Fry tortillas in batches, turning occasionally, until golden, about 1 minute, and transfer to paper towels to drain (return oil to 375 degrees F between batches). Carefully pour off all but 1 tablespoon hot oil into a large metal bowl to cool before discarding.
Preheat oven to 375 degrees F. Cook onion in oil in casserole over moderately high heat, stirring, until softened. Add broth and turkey and simmer, uncovered, stirring, until liquid is reduced to about 1/2 cup, about 15 minutes. Add 2 1/2 cups salsa and bring to a boil. Remove from heat and toss with Monterey Jack and tortilla strips.
Bake chilaquiles, uncovered, in middle of oven until bubbling, about 15 minutes. Whisk together creme fraiche and milk. Serve chilaquiles topped with creme fraiche, cilantro, and cheese.
If using fresh tomatillos, remove husks and rinse under warm water to remove stickiness. If using canned tomatillos, drain and measure out 2 cups. Broil chiles, garlic, and fresh tomatillos (do not broil canned) on rack of a broiler pan 1 to 2 inches from heat, turning once, until tomatillos are softened and slightly charred, about 7 minutes.
Peel garlic and pull off tops of chiles. Puree all ingredients in a blender.
Yield: 3 cups
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