Kavi

On why melted butter is not merely softer, which is the more interesting half of the question.

Butter is an emulsion — fat with water and milk solids dispersed through it — and it has a crystalline structure in the fat. Softened butter still has that structure, just warm enough to be pliable.

When you cream softened butter with sugar, the sugar crystals cut into that structure and trap air. Those tiny air pockets are what make a cake rise properly and give it its texture; the chemical raising agent expands existing bubbles rather than creating them.

Melted butter has lost the structure entirely. It cannot hold air, so creaming does nothing, and it also breaks the emulsion. The result is a denser, greasier, flatter bake — and it will not recover if you cool it again, because the crystal structure re-forms differently.

So "softened" is a specific physical state, roughly cool room temperature, and it is not a step on the way to melted.

One thing worth checking before assuming the butter is the problem: some recipes that call for softened butter work perfectly well with melted butter if you also change the method.

Melted-butter cakes and brownies exist and are excellent; they simply do not rely on creaming for lift. So if you have already melted it, look at whether the recipe's structure depends on creaming or on a chemical raise. If it is the latter, carry on.

What you cannot do is use melted butter in a creaming recipe and expect the same result.

It works, and your failure was an energy budget problem exactly as you suspected. The arithmetic is worth doing because it tells you the fix.

An egg is roughly 50 millilitres and starts cold. The water in the flask is the only heat source, and it gives up heat to warm the egg. The temperature they settle at is a weighted average, roughly by volume.

With a small amount of water and a cold egg, that equilibrium lands well below what is needed to set the yolk. With half a litre of boiling water to one egg, the drop is small — the mixture settles a few degrees below boiling, comfortably in cooking range — and a good flask holds that for a long time.

So the fix is: much more water relative to the egg, a properly preheated flask, and time. Rinse the flask with boiling water first and discard it, otherwise the flask itself absorbs a substantial share of your heat.

One thing worth noting about these cartons specifically: they are usually aseptically packed, which is why they sit on a shelf rather than in a chiller.

The contents were sterilised and filled in a sterile environment, so an unopened carton is stable at room temperature for a long time. Once opened, that protection is gone and it becomes an ordinary perishable — refrigerate and use within a few days.

That matters for your question because the difference between opened and unopened is not cosmetic. An opened carton that has been sitting at room temperature is genuinely a different proposition, and it is the reason the question is worth asking rather than being merely fastidious.

The more interesting point is the one hiding in your comparison of materials: most of ice's cooling power comes from melting, not from being cold.

Melting a gram of ice absorbs about eighty times the energy that warming a gram of water by one degree does. That latent heat is the whole reason ice works so well.

So a stone or metal cube, which only warms up and never melts, can absorb only a small fraction of what an equivalent piece of ice can. They keep a drink cool for a short time and cannot chill a room-temperature drink meaningfully. People who use them are choosing no dilution over actual cooling, and often do not realise how large that trade is.

A frozen spirit cube has the same limitation. It would melt, but a much smaller share of it and at a much lower latent heat, so the cooling is far weaker than water ice.

Which means the dilemma is real: dilution and cooling come from the same physical process, and you cannot have one without the other.

One small note on your method: warming honey to 50 degrees is fine for dissolving it, and much hotter would drive off some of the aromatic compounds that make single-flower honey worth using.

Many people now skip heat entirely and simply shake or stir the honey into cool water, which takes longer and preserves more character. Something to try on the next batch — and there should be a next batch, because the first one is mostly for learning what your equipment and your patience are like.