The Shulhan Aruch (O.H. 274:1) writes that one should recite the blessing of Hamotzi for the Shabbat meal over two whole loaves of bread. One should hold them both in one’s hands and then break off from the bottom loaf to eat and distribute to those present. The requirement for two loaves, known as Lehem Mishne, is derived from the extra portion of Manna that Bnei Israel received on Shabbat when they were in the desert.
A question arises as to whether Lehem Mishne applies to foods that are Mezonot. On one hand, if someone has a sufficient quantity of certain Mezonot foods, then it has the status of bread, and therefore it would seem that Lehem Mishne would apply. On the other hand, in its present state, the Mezonot is not actually bread and so Lehem Mishne might not apply. The Kaf Hahaim (K.H., O.H., 274:14) rules that Lehem Mishne does apply to Mezonot. Thus, if one wished to have Kiddush at synagogue with some Mezonot, for example, one could take two pieces of Bourekas or two danishes, and recite the blessing of Mezonot and also fulfil the Mitzvah of Lehem Mishne. Rabbi Ovadia Yosef (Hazon Ovadia, vol. II, pg. 191), argues and says that if one is not actually reciting the blessing of Hamotzi, then there is no Mitzvah of Lehem Mishne. Nevertheless, he continues, if it means he may lose out on Lehem Mishne, one may recite Hamotzi even over two slices or incomplete loaves of bread.
In certain cases, one only has one loaf of bread and the only other loaves one has are frozen. Rabbi Ben Zion Abba Shaul (Or Lezion, vol II, ch. 21, § 2) categorically permits the use of a frozen loaf since it has the status of bread and even though it is frozen in its current state, it can eventually thaw. Furthermore, if one is careful to only eat bread that is Yashan (made from wheat that took root before the 16th of Nissan of a particular year), then it is not permitted to use loaves that are not Yashan. However, if one is unsure whether the bread is Yashan or not, Rabbi Ben Zion Abba Shaul (ibid., vol. I) says one would be permitted to consumer it and all the more so on Shabbat when there is a special requirement to eat bread and of Lehem Mishne.
If one finds oneself in a situation in which one has a piece of bread for Hamotzi that is less than a Kezayit, the Siddur Bet Menuha (pg. 51), which was commonly used in Morocco says one fulfills one’s obligation with such a piece. On the other hand, Rabbi Haim Palagi (Kaf Hahaim, § 36:44 ), the Kaf Haim (ibid:8) ,and Rabbi Binyamin Pontrimoli (Petah Hadevir, § 6) disagree and say one would not fulill one’s obligation.
Summary: One should recite Hamotzi on Shabbat over two whole loaves of bread. If one will be eating Mezonot instead, there is no Mitzvah of Lehem Mishne. One ma use a frozen loaf of bread if needed to complete Lehem Mishne.