Combine the mussels, potatoes, and wine or water in a broad, steep-sided skillet or casserole. Cover and turn the heat to high. When steam arises from the top, shake the pan once or twice and turn the heat to medium. Continue to cook until all the mussels open, checking after five minutes or so and then every couple of minutes. When the mussels are done, use a tongs or slotted spoon to remove them to a plate; leave the potatoes in the skillet and recover.
2.
Cook until the potatoes are almost tender, then remove the cover and turn the heat to high, cooking until most of the liquid evaporates and the potatoes are done. By this time, the mussels will be cool enough to remove from their shells; do so, putting them in a large bowl.
3.
When the potatoes are done, add them to the bowl with the mussels and the shallots, oil, vinegar, salt and pepper. Taste and adjust seasoning as necessary. Serve immediately, an hour or two later, or cold, stirring in the herb(s) at the last moment.