In a dreamful manner; with a dreamy, imaginative, or distracted quality.
From dreamful (adjective) + -ly (adverbial suffix). The -ly suffix converts the adjective into an adverb describing manner or quality.
English speakers rarely use 'dreamfully' because 'dreamily' (from dream + -i + -ly) is shorter and sounds more natural—this preference for simpler, more euphonious words is why some perfectly valid formations disappear from use.
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