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1
Roast the chiles.
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2
Roast the poblanos directly over an open flame or 4 inches below a broiler, turning regularly until blistered and blackened all over, about 5 minutes for a flame, about 10 minutes for the broiler.
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3
Cover with a kitchen towel and cool until handleable.
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4
Rub off the blackened skin, then pull out the stem and seed pod.
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5
Briefly rinse to remove any stray seeds or bits of skin.
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6
Slice 1/4 inch thick.
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7
Brown the chicken.
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8
In a large skillet, heat the oil over medium-high.
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9
Generously sprinkle the chicken breasts with salt on both sides and lay them into the pan in a single layer.
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10
When browned underneath, about 4 minutes, flip them over and reduce the heat to medium.
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11
Cook on the other side until browned and medium-rare (a little slit in the thickest part will reveal a rosy interior), 5 or 6 minutes more.
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12
Transfer to a plate.
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13
Finish the dish.
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14
To the skillet (still over medium heat), add the onion.
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15
If there isnt enough oil to lightly coat the onion, add a little more.
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16
Cook, stirring regularly, until richly browned and sweet.
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17
8 or 9 minutes.
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18
Meanwhile, cut the chicken into 1/2-inch cubes.
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19
Add the garlic and chile slices to the skillet and cook 1 minute, then add the greens, broth and thyme (if you have it).
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20
Raise the temperature to medium-high.
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21
Cook until the liquid is nearly gone and the greens are almost tender, about 5 minutes.
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22
Add the crema, creme fraiche or cream and cook until it is noticeably thicker (itll be a rich glaze) and the greens are fully tender, about 5 minutes more.
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23
Taste and season the mixture in the skillet with salt.
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24
Usually 1/4 teaspoon.
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25
Stir in the chicken, let heat through for a minute or two, scoop into a serving bowl and enjoy without hesitation.
