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The Preface - hakdama to the English edition of Volume 1 of Shmiras Shabbos k'Hilchaso writes that if a Jew b'shogeg (mistakenly) plants or sows a seed on Shabbos, or anything like that where some time elapses after Shabbos before any benefit can be gotten from that melacha, then the result of that planting or sowing or whatever melacha is prohibited from benefit forever, because to prohibit the benefit for use only that Shabbos would not be penalising the violator at all, since in any case the object of the melacha would not be available for benefit until after Shabbos.
My question: Would the same rule apply to something that wouldn't take as long a time to complete, like b'shogeg cooking something or laundering clothes, if the person started the melacha close to the end of Shabbos but the cooking or laundering wasn't completed until after Shabbos was over. Would that food be prohibited forever just like the result of the planting?

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The Shulchan Aruch Orach Chaim 318,1 states that cooking or any other Melacha which a Jew does on purpose, though the one who did the melacha may not benefit for ever, others can benefit straight away after Shabbos:

המבשל בשבת (או שעשה אחת משאר מלאכות) במזיד, אסור לו לעולם ולאחרים מותר למוצאי שבת מיד

The Magen Ahvraham and Mishna brura explain:

דדוקא בעכו"ם שעושה בעינן בכדי שיעשה דחיישי' שמא יאמר לו לעשות אבל ישראל לא ישמע לו
Only when a gentile does a melacha for a Jew, one cannot benefit until that Melacha could be completed (e.g if he laundered your clothes you would wait the time it takes to launder your clothes) after Shabbos as we decree in case he asks the gentile to do malacha for him in the future, but if a Jew does a Melacha there is no decree to wait as we do not expect him to listen to another Jew to sin.

The Biur Halacha explains that planting/sewing seed are exceptional in that they are forbidden forever, all other regular Melacha that can potentially benefit on Shabbos are only prohibitted till Motzei Shabbos

ודע דלדעת השו"ע דפסק כר"י דבשוגג מותר ליהנות במו"ש זהו בכל מלאכות דמנכר הקנס שקנסו חז"ל שלא ליהנות בו ביום עד מו"ש אבל בנוטע בשבת וה"ה בזורע דבלא"ה אין יכול ליהנות לאלתר שוגג שוה למזיד דבשניהם צריך לעקור הנטיעה כן איתא בהדיא בגיטין נ"ד ע"ב
According to the Shulchan Aruch the very act of cooking/other Melacha it is clear that it could be completed and benefited from on Shabbos so the knas is not to benefit till Motzei shabbos unlike planting which takes months/years to benefit so the only Knas befitting would be to uproot the plant and not benefit after Shabbos at all if it was planted on Shabbos whether planted on Shabbos on purpose or by mistake.
So there is no difference between cooking just before Shabbos ends and cooking earlier in the day.

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