My Danish almond cake glaze just melted and never thickened. What went wrong?

At the point where it just turned to almonds and liquid, the almond most likely glaze wasn't ready; it required more cooking time to thicken.

If you can tell that it did thicken a little, it could be how it needs to cool for a while before it thickens, as that's what butter and sugar does when cooled.

If your glaze didn't "come together", you didn't overcook it, for sure. Instead most likely you never got everything hot enough to really melt the sugar.

So, what went wrong?

1. You didn't cook it long enough. Never mind the "three minutes", it takes whatever time is needed given the heat you use, the thickness of your pot and other variables. Cook it until it thickens. And keep stirring.

2. Your stove wasn't hot enough - try again with a higher setting. Your sugar+butter mixture should come to a boil, but not burn. Stir and keep stirring. Once it boils, it should be thickened. And, as you take it off the heat and pour it over your cake, it will thicken even further as the melted caramel cools.

..... You are making a glaze to cover, sweeten and protect your cake. Your goal is to combine sugar and butter into a gooey creamy stuff you can pour over your cake.

How do you do this? Just cooking butter long enough to melt it, isn't enough. Crystalized sugar doesn't dissolve in butter, not even hot, melted butter; it just swims around in the stuff, in little sandy crystals. That "liquid" you mention sounds like melted butter with sugar bits swimming about.

But if you get everything hot enough to melt the sugar, suddenly the melted butter will combine with it to make gooey caramel! Everything has to be hot enough, long enough to melt the sugar.