Heat 1 tablespoon vegetable oil in a large nonstick skillet over medium-high heat. Add the dumplings in a single layer. Cook until browned, 2 to 3 minutes per side. Add 1/4 cup water to the skillet. Cook, stirring occasionally, until evaporated, about 1 minute; transfer the dumplings to a bowl.
Heat 1 tablespoon vegetable oil in the skillet. Add the vegetables and cook, stirring occasionally, until crisp-tender and lightly browned, 8 to 10 minutes; transfer to the bowl with the dumplings.
Heat the remaining 1 tablespoon vegetable oil in the skillet. Add the shrimp, ginger and garlic. Cook, stirring occasionally, until the shrimp are just cooked through, about 2 minutes. Return the dumplings and vegetables to the skillet and stir to combine. Add the chili sauce and soy sauce; cook, stirring gently, until glazed, about 1 minute. Remove from the heat and stir in the rice vinegar and half of the scallions. Top with the remaining scallions.