[Moonman62]

Putt the vessell that hath the chocolate in it, into a jaraffa (carafe) of snow stirred together with some salt

Salted snow.

[Yardstick]

Salted snow would work but that doesn’t seem like cutting edge technology, even for the 16th century. I was hoping they had a crazy contraption with bellows and copper pipes that when driven by a team of 12 horses could chill a cup of chocolatti for the king and a few of his favorite courtiers.