Unless you prefer to do so, there's no need to remove the stems from the chard for this quick Asian-flavored stir fry.
Heat the sesame and peanut oils in a very large skillet or wok over medium heat. Add the garlic, ginger, and pepper flakes, and sauté for 2 or 3 minutes, stirring frequently. Don't let the garlic burn or it will become bitter.
Add the chard and soy sauce, raise the heat to medium high, and cover the pan. Cook the mixture, stirring occasionally, until the chard wilts, about 5 minutes. Remove the cover and add the mirin. Cook, stirring frequently, until the chard is tender, 5 to 10 minutes, depending on the maturity of the chard.
Transfer the chard to a serving platter and sprinkle with the sesame seeds. Serve hot.