In the manner or style of an engineer; with engineering skill, precision, or methodology.
From engineer plus -ing plus -ly, stacking two adverbial suffixes. This creates an adverb describing actions done with the approach of engineering.
This awkward-sounding word shows how English can create adverbs for almost any profession—'lawyeringly' or 'doctoringly' would follow the same pattern, though nobody actually uses them!
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