In a growling manner; speaking or acting in a grumpy, complaining way.
From 'growl' plus the present participle '-ing' plus the adverbial suffix '-ly.' The '-ly' suffix comes from Old English 'lic' meaning 'like' and creates adverbs from adjectives.
Many English adverbs follow this '-ing' + '-ly' pattern (confusingly, mockingly, laughingly), which lets us describe exactly HOW someone does something—'he growlingly refused the invitation' tells us his attitude instantly.
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