A desert is an arid region often associated with sand dunes and hot weather, although several deserts are in fact void of sand and are very cold.
A dessert is a tasty after-dinner treat consisting most often of something sweet.
People often mistake the two because they sound alike but are spelled differently.
To get your “just deserts” is a phrase that doesn’t help matters. It means to get one’s apt reward or punishment — as one deserves. It means neither you’ll just get an arid landscape or an apple pie. Often, restaurants will “cleverly” name their business “Just Desserts” as a pun to draw a clientele who find this sort of thing witty. In fact, the word comes from “deserve.”
Who, I wonder, deserves this Baked Prune Whip?
The Miracle Blender Cookbook: The Fine Art of Modern Blending, Tested Recipe Publishers, 1967
Also from this book: The Miracle of Blending!