In a glazy manner; with a glassy, smooth, or dull appearance or quality.
From 'glazy' plus the adverbial suffix -ly, which transforms adjectives into adverbs describing how something is done or appears. This follows standard English word-formation patterns.
When someone's eyes look 'glazily' unfocused during a boring lecture, you're literally using a word that connects to the same root as medieval stained glass—language beautifully recycles metaphors from craftsmanship.
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