Why did my nougat burn?
Your recipe is broken. If it actually gave you that temperature then discard it and find a new one.

Nougat is made, depending on the recipe, by heating the syrup to "hard ball" or "soft crack" temperatures before beating it into the egg whites.

Candy temperatures are categorized by the behavior of the syrup when dripped into ice water.

Hard ball is around 250F (121C) and looks like this:


Your temperature of 327F (164C) is actually off the chart and is categorized as "caramel" because the syrup has started to break down and the sugars are burning. Caramels have a lovely flavor but it is not going to create the correct texture for nougat. There is also a very fine line between "light caramel" and "horribly burnt" that is best avoided.

I recommend you find a more reasonable recipe.