What went wrong making hollandaise and how do I fix it?

[KevinAW]

I just tried to make a simple hollandaise for the first time and it completely broke on me, turning into a greasy, curdled mess. I was so careful with the heat and whisking, but I think I might have added the butter too fast?

[Adam.H]

That happened to me once with the same simple sauce I thought the heat was steady and then I poured the butter too fast and watched the emulsion split the pan was a touch hot and the whole thing went greasy

[Ava10]

I tried to salvage it by whisking and I added a teaspoon of warm water to see if it would smooth out and for a moment it looked glossy then it slid back into separation which felt like a small win and then a loss

[Aubrey.S]

I kept thinking about the moment I hit the switch on the stove and the butter started passing from pale yellow to greasy and I wandered into the kitchen thinking maybe I should switch to a quick lemon butter sauce but I kept coming back to the same heat idea

[Emma94]

Do you think the real problem is the temperature of the eggs or did the butter pour just too fast