This familiar expression meaning a deserved outcome or comeuppance is often misspelt as desserts and indeed Just Desserts is the title of a recipe book on puddings by Gordon Ramsay. Just deserts is not a famous quotation either. It is simply a word construction similar to just reward. Desert is an old English word from the French deservir meaning to deserve. Desert meaning something that is deserved made its first appearance in the Middle English period 1150-1450. It is now largely obsolete except in the form of this common expression that has lingered on to the point of cliché.