Place the unpeeled potatoes in a steamer basket set over boiling water. Steam for 7-8 minutes until just tender. Remove from the basket and leave until cool enough to handle.
Meanwhile, heat the olive oil in a non-stick frying pan. Add the onions and gently fry over medium heat for about 10 minutes until soft but not browned. Lightly season with salt and dot with the butter.
Peel off the potato skins and slice the flesh into 1/2in discs.
Arrange in a layer on top of the onions. Scatter with basil and season with a little more salt.
Whisk the eggs well with a good scrunch of freshly ground pepper. Pour them over the potatoes and onions.
Cover the pan and cook over low heat for about 15 minutes, or until the eggs are completely set. Season with a little more salt.
Flip the omelette over onto a large plate, then slide it back into the pan. Brown the underside for a minute or two.
Remove the pan from the heat and leave to rest for a few minutes.
Slice into segments and serve. Or, if you are heading for the blue yonder, allow your creation to cool before wrapping it in a large sheet of foil lined with greaseproof paper.