In a manner that is somewhat beam-like; with a bright, cheerful quality.
From 'beamish' (beam plus -ish) plus the adverbial suffix '-ly,' creating a double-suffixed adverb that intensifies the descriptive quality of brightness and cheer.
This is what happens when English speakers get creative: you can stack suffixes like building blocks to create words that feel right even if they're rare. It's the linguistic equivalent of emphasizing something by saying it with extra enthusiasm.
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