Ah, what Kei-san says is much closer than mine to the asker's point in terms of the word order : ～なくてもつくれる。 Great :)

This appear in sentence ~ なくても～できる　your example of translathing as my translation of to do not essential (compulsory) for cook(make ) fit for this word coming before something should be the item is not compulsory item Ex, If I make hamberger Onion is not essential for making that (もし　わたしがハンバーガーをつくるなら、わたしはオニオンがなくてもつくれる）　this ~ なくても～できるは”　did not mean Not Need" this means is Not compulsory If caming front of sentance "Onion is not compulsory for making Hanbarger " ハンバーバーはオニオンがなくてもつくれる。 "Objects is not compulsory for making sentance" 文は目的語がなくてもつくれる＝（目的語は文のひっすう(ようそ）ではないObject is not compulsory(item) for making sentence ) you understand diffence between to need and to be compulsory .

I clicked on the wrong icon but this is my answer, not comment.

You seem to understand that correctly to me. What's so confusing to translate? I can make a cup of coffee without sugar. (=I don't need sugar to make a cup of coffee.) 砂糖がなくてもコーヒーはつくれる。 I can make carry and rice without potatoes. (=I don't need potatoes to make carry and rice) ジャガイモがなくてもカレーライスはつくれる。 I can make a sentence without the object. 目的語がなくても文はつくれる。 But you might need an objective word and a particle before つくれる in order not to be ambiguous depending on what you mean. And before なくても as well.