In a grum manner; with a morose, surly, or withdrawn demeanor.
From grum (morose) plus -ly (adverbial suffix), creating an adverb that describes how someone acts or speaks with gloominess and ill-humor.
British English has these wonderful -ly adverbs from descriptive adjectives that Americans might convert to 'in a [adjective] way' instead—'grumly' is more economical and sounds more period-appropriate in novels set in Britain.
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