Cut the potatoes into quarters and put them in a large pot of cold water. Bring the water to a boil and add a generous heap of salt (like a tablespoon). Simmer until tender then drain.
Put the aquafaba in a tall cup and insert an immersion blender. With the blender running, slowly drizzle in the oil until it thickens into a mayo. It’s important to do this very slowly to prevent the mayo from breaking. Obviously skip this step if you’re using store-bought mayo.
Stir the barbecue sauce, mustard and ½ teaspoon of salt into the mayo.
Once the potatoes are cool enough to handle, you can peel them if you want to (I didn’t) and chop them into smaller cubes. Since aquafaba mayo tends to melt over hot food I like to let the potatoes cool completely before putting together the salad.
Toss together the potatoes, gherkins, green onions, dressing and pepper. Taste and add more salt if you think it’s necessary. Serve immediately or refrigerate for later.