Huh, so even though Nigdy is negative, you still have to say "nie" as well? "One nigdy gotują" wouldn't work?
No. with words like nigdy=never , żaden=none, nic=nothing , nikt=nobody etc you need to use "nie"
It's just one the peculiarities of the Polish language that you gotta use a double negation. If you use it the way you suggested, it is clearly a mistake and would be noticed right away by a native speaker.
In my language we would usually put the sentence like this: one nie nigdy gotują. Does this order works in Polish as well?
No. That would be like saying "not never" in English. What you negate is cooking, so 'nie' has to come in front of it.