Step 1 Roast the chiles over a gas flame or under the broiler until the skins are evenly charred on all sides. Let cool, then slip off the skins and stems and scrape out the seeds. Cut the flesh into a fine dice and set aside.
Step 2 Remove the stems from the Swiss chard leaves, reserving them for another use. Wash the leaves in two or three changes of cold water. Cut the leaves crosswise into thin strips and set aside.
Step 3Cut the shiitakes in half and then crosswise into thin strips.
Step 4In a very large skillet (or use two skillets), heat the oil over medium heat. Add the garlic and saute, stirring constantly, until just softened, 3 to 4 minutes. Add the shiitakes and cook, stirring often, for 10 minutes. Start adding the chard, a handful at a time, stirring and cooking until the leaves soften enough to allow more leaves into the pan. Continue until all the chard is in the pan.
Step 5Raise the heat to medium-high and stir in the tamari or soy sauce. Add the poblanos and mix well. Add the stock and cook, stirring, until all the ingredients are well mixed. Continue cooking, stirring occasionally, until the chard is completely tender, about 15 minutes.