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The words 

“deserve” and “dessert” are connected through a common French root and an old noun form of the verb “to deserve,” called “desert”. While they sound identical in the phrase “just deserts” (meaning what one has earned or what is rightfully due), the confusion comes from the similar spelling to the sweet food item, “dessert”. 

Shared origin

• Both words ultimately derive from the Old French word deservir, meaning “to serve well”.
• From this root, the verb “to deserve” (to earn or merit) came into English, while a related noun form also emerged. 

The phrase “just deserts”

• The correct spelling for the phrase meaning “what one deserves” is “just deserts,” pronounced like “desserts”.
• “Desert” in this case is the archaic noun form of the verb “to deserve”.
• It can refer to either a reward or a punishment.
• The confusion arises because the pronunciation is identical to the food item “dessert,” which also comes from a French root (desservir) meaning “to clear the table”. 

Modern usage

• While the noun “desert” is rarely used today except in the phrase “just deserts,” the verb “deserve” remains common.
• Many people incorrectly write “just desserts” because it makes intuitive sense to them, linking deserved punishment or reward with a literal sweet treat.