In a babblish manner; in a way that somewhat resembles or tends toward babbling or incoherent speech.
From 'babblish' plus the adverbial suffix -ly. This represents a more indirect formation than 'babblingly' (babble → babbling → babblingly), adding an extra layer of qualification through the -ish suffix.
The fact that you can say something either 'babblingly' or 'babblishly' shows English's flexibility—the first is direct, the second more qualified and gentle, giving speakers nuanced options for the same basic meaning.
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