Heat vegetable oil in a 12-inch nonstick skillet over medium-high heat until hot, then arrange dumplings, slightly overlapping, in a spiral pattern and fry until bottoms are pale golden, 2 to 3 minutes. Add water, tilting skillet to distribute, then cover tightly with lid and cook until liquid has evaporated and bottoms of dumplings are crisp and golden, 6 to 7 minutes. (Use a spatula to loosen and lift edges to check bottoms; replace lid and continue cooking if necessary, checking after 1 to 2 minutes.) Remove lid and invert a large plate with a rim over skillet. Holding plate and skillet tightly together, invert dumplings onto plate. Serve immediately, with dipping sauce.