In a manner that causes or expresses cringing; in a way that is embarrassing or uncomfortable.
Cringe plus the adverbial suffix -ly, which converts adjectives and verbs into adverbs describing how something is done.
The suffix '-ly' is so common in English that we barely notice it, but it's one of the most productive word-building tools in the language—you can make an adverb from almost any adjective, which is why 'cringingly' feels natural even if you've never heard it before.
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