The story
Unadapted borrowing from Italian tagliatelle, from tagliare (“to cut”). * In Italian, -gli(a)- is pronounced /ʎ-/, which can be approximated in English by /lj-/; the pronunciation with /ɡ/ is a spelling pronunciation. * In English, the final vowel is most often /i/, and only rarely /eɪ/ (the expected approximation of Italian /e/, as in e.g. bersagliere), probably due to the prevalence of Italian terms ending in /i/ (cavatelli, ravioli, etc).
Etymology from Wiktionary, CC BY-SA 4.0.