Having been heated until browned and crisp, or slang for being intoxicated or in trouble.
From Middle English tosten, from Old French toster 'to roast, toast', ultimately from Latin torrere meaning 'to parch, burn, or dry'. The drinking toast sense came from the practice of putting spiced toast in wine.
The connection between bread toasting and drinking toasts comes from 17th-century taverns where spiced toast was dropped into wine for flavor. The slang meaning 'drunk' or 'in trouble' plays on the idea of being 'heated up' or 'cooked'—a perfect example of metaphorical language evolution.
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