Step 1

Roast the chiles. 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. Cover with a kitchen towel and cool until handleable. Rub off the blackened skin, then pull out the stem and seed pod. Briefly rinse to remove any stray seeds or bits of skin. Slice ¼ inch thick.

Step 2

Brown the chicken. In a large skillet, heat the oil over medium-high. Generously sprinkle the chicken breasts with salt on both sides and lay them into the pan in a single layer. When browned underneath, about 4 minutes, flip them over and reduce the heat to medium. 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. Transfer to a plate.

Step 3

Finish the dish. To the skillet (still over medium heat), add the onion. If there isn’t enough oil to lightly coat the onion, add a little more. Cook, stirring regularly, until richly browned and sweet. 8 or 9 minutes. Meanwhile, cut the chicken into ½-inch cubes.

Step 4

Add the garlic and chile slices to the skillet and cook 1 minute, then add the greens, broth and thyme (if you have it). Raise the temperature to medium-high. Cook until the liquid is nearly gone and the greens are almost tender, about 5 minutes. Add the crema, crème fraîche or cream and cook until it is noticeably thicker (it’ll be a rich glaze) and the greens are fully tender, about 5 minutes more.

Step 5

Taste and season the mixture in the skillet with salt. Usually ¼ teaspoon. Stir in the chicken, let heat through for a minute or two, scoop into a serving bowl and enjoy without hesitation.

Step 6

Working Ahead:The poblano can be prepared and the chicken cooked a day or so ahead; store separately, well covered, in the refrigerator. Pick up the preparation at Step 3 shortly before serving.

Step 7

Mexican Crema:A tub of crème fraîche will provide you the closest thing to real Mexican crema, since, to my knowledge, there are no artisanal Mexican dairies producing high-quality traditional creams and cheeses in wide distribution in the United States. Crème fraîche and crema are essentially the same, meaning that they are both cultured creams and that there is a lot of variety from brand to brand, region to region, season to season.You can culture your own crema using the long-standing recipe: Add 1 tablespoon live-culture buttermilk to 1 cup heavy cream slightly warmed to 80 degrees. Let stand until thickened (usually 6 to 12 hours) at warm room temperature, refrigerate until very thick. It’s complexly delicious and nutty-tangy and much less expensive than a tub of crème fraîche. But it will quickly melt into a puddle when you spoon it on anything warm.To avoid the quick melt, you can make your crème fraîche with the sour cream alternative: Mix equal parts of very good quality sour cream and heavy cream, let stand at warm room temperature until noticeably thicker (about 6 hours), then refrigerate for several hours until very thick. This version isn’t as nutty as crème fraîche, but it’s rich, tangy and substantial enough to stand up to warm foods.