1½ pound) poblano chiles
3 tablespoons olive oil
2 pounds (16 medium) tomatillos , husked, rinsed
2 large white onions, chopped (3 cups)
4 large cloves garlic, unpeeled
24 corn tortillas
2 cups chicken broth
½ cup chopped fresh cilantro
1½ teaspoons salt
1 cup crème frâiche -or- sour cream
6 cups shredded roast chicken (from 2 roast chickens)
1 pound (4 cups) shredded Monterey Jack cheese
Heat broiler. Place chiles on a baking sheet; lightly brush with 1 tablespoon of the oil. Broil as close to the heat source as possible, 8 to 10 minutes, turning frequently, until skins are blackened all over. Transfer to a plastic food storage bag or paper bag; let cool. Scrape off charred skins; cut off stems, halve chiles, and remove seeds; coarsely chop.
Place tomatillos and garlic on broiler pan rack; broil close to heat source, 15 minutes, turning frequently, until tomatillos and garlic are charred in spots and soft. Remove skins from garlic and chop.
Heat remaining oil in a large Dutch oven over medium-high heat. Add onions; cook 8 minutes. Add chiles, tomatillos, garlic, 2 corn tortillas, torn into small pieces, and broth. Bring to a boil, reduce heat, and simmer 10 minutes. Remove from heat; when cool enough to handle, transfer mixture to food processor with cilantro and salt; pulse until sauce is just slightly chunky. Transfer to a bowl; whisk in crème frâiche until blended.
Spread ¾ cup of sauce thinly on bottom of 2 (13x9x2-inch) baking dishes. In a large bowl, combine chicken with 1 cup sauce and toss to lightly coat (sauce can be made up to 2 days ahead and refrigerated; thin with more broth or water before using).
Heat oven to 350 degrees F. Stack 11 of the remaining tortillas on a microwave-safe plate and cover with a moist paper towel. Microwave 1 minute, until heated through and pliable. To assemble enchiladas, dip a tortilla into sauce just to moisten and top with a heaping 1/4 cup chicken mixture and 2½ tablespoons cheese. Roll up tortilla snug and transfer to a baking dish. Repeat with remaining 10 tortillas.
Soften remaining tortillas in microwave and assemble second baking dish with enchiladas. Spoon remaining sauce and cheese over top of enchiladas. (Can be covered and refrigerated up to 1 day ahead; bring to room temperature before baking.)
Bake 20 minutes, or until heated through and sauce is bubbly. Remove enchiladas from baking dishes with a spatula and serve immediately.