Chefs & Cooks - Which is correct?

I have heard both and I think both are acceptable.
Sort of depends on how you were taught or where you came from.
Much like pronouncing Aunt. Many say "Ant" I say "Aunt"... Ants are little things that crawl on the ground and come uninvited to a picnic.
Lots of other words have two or more acceptable pronunciations.

'cull' not the strong 'k' sound
the rest is
'in' - 'arry' (like in Barry)

I have always used Kulinary, but both pronunciations can be considered correct.