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If the person definitively intended to eat only one portion and only afterward changed his mind, he must recite the blessing of “Borei Minei Mezonos” over the additional portion, because one slice does not constitute a full established meal (keviut seudah). However, he must recite Birkat HaMazon as his after-blessing. Even though this is a highly unique halachic scenario—where one recites Borei Minei Mezonos as the before-blessing but concludes with Birkat HaMazon—such is the halacha.
However, if a tray is in front of him and he decides to eat two more portions, or one more portion along with cakes, such that the total amount he is about to eat reaches 230 grams—he is obligated to wash his hands and recite the blessing of “Hamotzi”. The Birkat HaMazon he recites at the end will then cover the first slice of pizza eaten prior to washing his hands (Shulchan Aruch HaRav, Siman 168).
The Igros Moshe (Orach Chaim, Part 2, Siman 54) discusses the reverse situation, where a person washed his hands intending to eat two slices of pizza but changed his mind halfway through. He rules that the person may continue eating and rely on the Hamotzi blessing he made at the beginning. However, for his after-blessing, he must recite “Al HaMichyah”. This represents another exceptional halachic ruling, where one recites Hamotzi at the beginning but concludes with Al HaMichyah.