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Make the sauce– Roast the poblanos directly over a gas flame or a baking sheet 4 inches below a very hot broiler.
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Turning regularly, until the skins have blistered and blackened on all side, about 5 minutes for an open flame, about 10 minutes under the broiler.
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Cover with a kitchen towel and, when handleable, rub off the blackened skin, tear open and pull out the seed pod and stem.
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Quickly rinse to remove any stray seeds or bits of skin.
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Roughly chop and put in a blender jar.
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Add the spinach.
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In a medium (3quart) saucepan, combine the milk and broth, set over medium-low heat to warm.
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In a large (4quart) saucepan, melt butter (or heat the oil) over medium heat.
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Add the garlic and cook for a minute to release its aroma, then add flour and stir the mixture for a minute.
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Raise the heat to medium-high.
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Pour in the warm broth mixture and whisk constantly until the sauce boils.
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Reduce the heat to medium and simmer for 5 minutes.
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Remove from the heat.
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Pour half the hot sauce into the blender with the chiles and spinach.
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Cover loosely (I remove the center part of the lid, secure the lid, then drape a cloth over the whole thing.) and blend until smooth.
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Pour the mixture back into the saucepan with the remaining sauce.
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Taste and season well with salt, usually about 2 teaspoons.
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Finishing the enchiladas– Heat the oven to 350 degrees. smear about 1/4 cup of sauce over the bottom of each of four to six 9inch individual oven proof baking/serving dishes ( for individual servings)– or smear about 1 cup of the sauce over the bottom of a 13×9 inch baking dish (for family serving).
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Stir 1 cup of the sauce into the chicken.
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Lay half of the tortillas out on a baking sheet and lightly brush or spray both sides of the tortillas with oil; top each tortilla with another one and brush or spray those with oil.
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Bake just until warm through and soften, about 3 minutes.
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Stack the tortillas and cover with a towel to keep warm.
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Working quickly so that the tortillas stay hot and pliable, roll a portion of the chicken up in each tortilla, then line them all up in the baking dish or dishes.
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Douse evenly with the remaining sauce and sprinkle with the cheese.
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Bake until the enchiladas are hot through (the cheese will have begun to brown) about 20 minutes.
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Garnish with the cilantro and serve without hesitation