I did not have milk or milk powder on that day and from my experience, most bread recipes would have milk in its ingredients list, otherwise, the softness usually do not last for more than a day.
I fall back on this chocolate chip buns recipe . This produces bread which remained soft for at least 2 days and does not has milk. Probably the eggs in tis case adds richness to it. But be prepared to handle a rather sticky dough.
I merely omitted the cocoa powder and chocolate chips, and baked them in a loaf tin instead of shaping them into individual buns.
I realised how important It is to keep some good to-keep recipes for the same baked item (e.g. basic white bread, basic muffin or cakes) because you may just have one ingredient and not the other. That's when we can make good with whatever we have and still have your favourite baked goods without having to buy that ingredient solely for that purpose. :)