This year (5782), the seventh day of Pesach will fall out this coming Friday. The next day will be Shabbat.
One should therefore take care to prepare an Eruv Tavshillin on Erev Yom Tov (Thursday), as we have explained in the previous Halacha.
Cooking Kitniyot on the Seventh Day of Pesach
Ashkenazim customarily abstain from eating Kitniyot (legumes) on Pesach as we explained before the holiday; some Moroccan communities adopted a similar stringency. Some only abstain from eating rice but not other legumes. This year when the seventh day of Pesach falls out on Erev Shabbat, the question becomes, as follows:
Question: Is it permissible to cook rice on the seventh day of Pesach in order to serve it the next day on Shabbat? (This question applies only in Israel when the last day of Pesach is on Friday and the following day is a regular Shabbat. Outside of Israel though, this coming Shabbat will still be the eighth day of Pesach.)
Answer: Although there are those who customarily abstain from eating Kitniyot on Pesach, they do not consider it as prohibited as actual Chametz. It is for this reason that even Ashkenazim are permitted to retain Kitniyot in their possession on Pesach. The same applies to baby formulas containing Kitniyot ingredients in that everyone allows using them on Pesach with designated utensils.
Thus, halachically speaking, it is permissible for an Ashkenazi to cook Kitniyot on the Yom Tov of the seventh day of Pesach (obviously, only when having prepared an Eruv Tavshillin). The reason for this is because Sephardic Jews who customarily consume Kitniyot on Pesach are quite common in most Jewish metropolises and thus, it is possible that a Sephardic Jew may arrive at the home of an Ashkenazi and they would then be able to serve him the Kitniyot dishes. Thus, since there is a possibility of using this dish on Yom Tov itself, there is no reason to prohibit Ashkenazim from cooking Kitniyot on Yom Tov, although they customarily prohibit their consumption.
Although Rabbeinu Yosef Haim zt”l rules stringently on this matter because of cooking on Yom Tov and the Responsa Halachot Ketanot rules stringently for another reason, nevertheless, there is room for leniency in Israel. Indeed, Hagaon Harav Shlomo Zalman Auerbach zt”l rules leniently in his Responsa Minchat Shlomo (Volume 2, Chapter 17), as do many great Poskim. It is preferable that if this is done, the Kitniyot should be cooked in designated vessels and using special utensils, for Ashkenazim customarily do not use their Pesach dishes for cooking Kitniyot. However, this will be permissible when using other dishes.
Summary: An Ashkenazi who customarily abstains from eating Kitniyot on Pesach may cook Kitniyot on the seventh day of Pesach in designated vessels for consumption on the Shabbat following Pesach (in Israel only).