The “EY” rhymes with the word “bay.” The “k” is softer than an English “k,” almost like a hard “g.” And the “t” at the end kind of sticks for a second and pulls away with a hint of a glottal “l.”
But it seems even the NYT may be incorrect. From YouTube - you're doing it wrong
Say it soft and it’s almost like, “Hey, ya fergot La Yogurt.”
“The first problem for Americans is, you see this long word and don’t know where to begin, “ said Joan Maling, a professor emerita of linguistics at Brandeis University. “You don’t know how to divide it up.”
It’s simple. “Eyja” is the Icelandic word for island. “Fjalla” means mountain. “Jokull” is glacier.