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Make the Cooked Green Salsa:
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Put the tomatillos and jalapenos in a medium saucepan, pour in enough cold water to barely cover (about 3 1/2 cups), and bring to a boil.
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Cook until the jalapenos are soft and the tomatillos are tender, about 20 minutes.
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Remove from the heat and let stand for 15 minutes to finish cooking the inside of the tomatillos.
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Drain the tomatillos and chiles (gently, to aviod breaking up the tomatillos) in a colander.
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Wipe out the saucepan and set aside.
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Put the tomatillos, jalapennos, garlic, and cumin in a blender jar and blend for a few seconds, just until the tomatillos are coarsely chopped.
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Add the cilantro (see Notes) and blend until the sauce is smooth and speckled with finely chopped cilantro.
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Do not overblend, or you will grind the tomatillo seeds and make a thick and pasty rather than smooth and shiny sauce.
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Heat the oil in the cleaned pan over medium heat.
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Pour in the salsa, bring to a simmer, and simmer until lightly thickened, about 10 minutes.
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Season with the salt.
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The sauce can be stored in the refrigerator for up to 3 days.
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Reheat over low heat before using.
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Preheat the oven to 375F.
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Make the enchilada sauce:
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Pour half the green sauce into a blender jar, add the poblanos, and blend at low speed until smooth.
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Pour into a medium saucepan, add the remaining green sauce and the cream, and bring to a simmer over low heat.
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Remove from the heat.
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If prepared in advance, reheat, adding water 1 tablespoon at a time if necessary to return the sauce to the right consistency, before ladling over the enchiladas.
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If using store-bought tortillas, soften in the oil and drain them.
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Fill and roll the tortillas, using 1/3 cup of the chicken for each one.
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Place the enchiladas seam side down in a 9 by 13-inch baking dish.
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The enchiladas can be prepared to this point up to 4 hours in advance.
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Cover them with a damp kitchen towel or paper towels, cover the dish with plastic wrap, and refrigerate.
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Remove from the refrigerator 30 minutes before baking.
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Pour the hot sauce over the enchiladas.
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Jiggle the dish so the sauce settles in between the enchiladas.
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Sprinkle the cheese evenly over the top.
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Bake until the sauce around the edges is bubbling and the cheese is golden brown, about 20 minutes.
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Let stand for 5 minutes before serving.
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Scatter the onion and cilantro over the enchiladas.
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Scoop 2 enchiladas and plenty of sauce onto each serving plate.
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VARIATION: Green Salsa For the Table.
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Coarsely grind 2 roasted and peeled jalapenos with a large pinch of salt in a molcajete or in a mortar with a pestle.
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Stir in 2 cups cooled Cooked Green Salsa, 1/2 cup finely chopped white onion, 1/2 cup chopped fresh cilantro, and salt to taste.
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(Alternatively, blend the chopped jalapenos and sauce in a blender jar using quick on/off pulses just until the jalapenos are coarsely chopped.
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Scrape into a bowl and stir in the onion, cilantro, and salt.)
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Let stand for 1 hour before serving.