Trim the eggplant and cut it into 1-inch cubes. (If the eggplant is large, sprinkle with salt, put in a colander, and let it sit for at least 30 minutes, preferably 60. Rinse, drain, and pat dry.)
Bring a large pot of water to a boil and add salt. Immerse the eggplant in the boiling water and cook until tender, about 5 minutes. Drain well and set in a colander to cool. (You can refrigerate the eggplant, covered, for up to a day at this point. Bring it back to room temperature before proceeding.)
Dry the eggplant with paper towels. Whisk together the miso, soy sauce, and mustard in a serving bowl. Add the eggplant along with salt and cayenne, then toss. Taste and adjust the seasoning if necessary. Serve with the lemon wedges.
