It can be tempting to cut skirt steak with the grain, but for a more tender chew, cut the steak into 4-inch pieces and then slice against the grain. For a spicy kick, add a diced red chile to the teriyaki sauce.
Prepare the rice according to the package directions.
Combine the soy sauce, brown sugar, salt, garlic, ginger and 2 tablespoons water in a small saucepan set over medium-low heat. Cook, stirring occasionally, until the sugar dissolves, 2 to 3 minutes. Remove from the heat and set the sauce aside.
Meanwhile, cut 4 of the scallions into 2-inch lengths. Finely chop the remaining scallion and set aside for serving.
Strip the chard leaves from the stems. Thinly slice the stems and roughly chop the leaves, keeping them separate.
Heat the oil in a large cast-iron skillet over medium-high heat until very hot. Add the 4 scallions and chard stems and cook, stirring, until just starting to wilt and pick up color, 2 to 3 minutes. Add the steak to the skillet and cook, stirring occasionally, until the steak is browned, 3 to 4 minutes. Remove from the heat. Add the sauce and chard leaves and stir until the chard just wilts.
Divide the rice between two bowls and spoon the stir-fry over the top. Sprinkle with the finely chopped scallion and sesame seeds.