In a manner showing complete attention, absorption, or fascination with something.
From engross (to absorb completely) + -ed (past participle/adjective marker) + -ly (adverb suffix). The structure transforms a verb into a manner-describing adverb.
Adding '-ly' to an already intense verb like 'engrossed' creates this perfect word for describing that moment when someone is so absorbed they don't hear you calling their name—we've all been engrossedly lost in something.
Complete word intelligence in one call. Free tier — 50 lookups/day.