Bring 1 cup water to a boil, remove from heat, and add salt. Stir until dissolved, then stir in sugar and vinegar. Pour brine into a shallow glass or nonreactive container with a lid. Press the mustard greens into the brine, then add enough cold water to cover the greens. Cover the container and leave at room temperature for 3 days. (Or, you can buy pickled mustard greens from a Chinese grocery store.)

Remove the greens from the brine, drain, and store in a glass jar in the refrigerator for up to 2 months. When ready to prepare the squid, rinse enough of the greens to get 2 cups, cut into 1/2-inch slices on the diagonal. Save any remaining pickled greens for another use.

Heat a wok or large skillet over high heat, add 2 tablespoons of the peanut oil and swirl to coat. Add the squid and stir-fry just until it curls and turns opaque, about 1 minute. Remove squid and drain on paper towels. Add the remaining 2 tablespoon oil to the wok, then add the pickled mustard greens, and the ginger. Stir-fry for about 30 seconds, then add the remaining ingredients. Stir-fry until mixture thickens slightly, about 2 minutes, then add the reserved squid, and stir-fry to heat through. To serve, transfer ingredients to a large platter and serve with rice noodles