Toast salt in a dry, small, heavy skillet over moderate heat, stirring, until the salt turns light tan, about 7 minutes. Transfer salt to a bowl.
Toast Szechwan peppercorns in skillet over moderate heat, stirring, until fragrant, about 2 minutes. Transfer toasted peppercorns to a sheet of waxed paper to cool. Using paper as a funnel, pour toasted peppercorns into an electric coffee/spice grinder or a mortar. Add pink peppercorns and pulse or pound with a pestle until finely ground. Pour through a coarse sieve into bowl of salt and stir together.
Cook edamame in salted boiling water until tender, about 4 minutes, and immediately transfer with a slotted spoon to a bowl of ice and cold water to stop cooking. Drain in a colander and pat dry.
Toss edamame with some peppered salt, to taste, and serve with remainder on the side.
Cooks' notes: Peppered salt may be made 1 week ahead and kept in an airtight container at cool room temperature. Edamame may be cooked 1 day ahead and chilled, covered. Bring to room temperature before tossing with peppered salt.