Prep the skewers. Soak bamboo skewers in water for 15 minutes so the ends do not scorch. Pat the thawed pods completely dry with a towel, then push 5 pods onto each skewer so they lie flat side by side.
Prep the chard and glaze. Cut the stems away from the leaves. Slice the stems into 1/2-inch (1 cm) pieces and cut the leaves into 2-inch (5 cm) ribbons. Rinse the leaves and shake off only the loose water, since the leftover water will steam them later. Whisk the 2 tablespoons soy sauce, honey and red pepper flakes in a small bowl.
Sear the first batch. Heat a 12-inch (30 cm) skillet over medium-high heat for 2 minutes. Add 1 tablespoon of the neutral oil, then lay 4 skewers in a single layer. Cook for 2 to 3 minutes per side without moving them, until the pods are blistered with brown spots.
Glaze and repeat. Move the skewers to a plate and brush them with half of the glaze. Using tongs, wipe the pan with a paper towel, add the remaining neutral oil, and sear the second batch the same way. Brush with the rest of the glaze.
Cook the stems. Wipe the pan once more with tongs and a paper towel, leaving a thin film of oil, and lower the heat to medium. Add the sesame oil, chard stems and salt. Cook for 4 minutes, stirring often, until the edges look glossy and a fork slides in with slight resistance.
Add the garlic and ginger. Stir them in and cook for 30 seconds, until fragrant and not browned.
Wilt the leaves. Add the leaves in three handfuls, tossing until each batch collapses before adding the next, about 2 minutes. Pour in the 1 tablespoon soy sauce and the water, cover, and cook for 3 minutes, until the leaves are dark green and tender.
Add the shelled edamame. Remove the lid, stir in the frozen shelled edamame, and cook for 3 minutes, until the beans are bright green and hot all the way through and the pan is nearly dry.
Finish and serve. Take the pan off the heat and stir in the rice vinegar. Taste and add a pinch of salt if needed. Lay the skewers on top, sprinkle with sesame seeds and scallions, and serve right away.