The Gemara in Masekhet Pesachim (120a) establishes that although the Torah writes that we are to eat matza for the seven days of Pesach (“Shivat yamim matzot tokheilu” – Shemot 12:15), this does not mean that one is actually required to eat matza for all seven days. The obligation to eat matza applies only on the first night of Pesach, whereas throughout the rest of Pesach, eating matza is optional. Of course, we must refrain from eating chametz throughout the seven days of Pesach, but the obligation to eat matza applies only on the first night.
The Vilna Gaon is famously cited as having asserted that eating matza on Pesach after the first night fulfills a mitzva, despite its not being obligatory (Ma’aseh Rav 185). The Torah does not require one to eat matza beyond the first night, but we nevertheless fulfill a Biblical mitzva by doing so.
This view appears in the works of several other Acharonim, as well, including the Avnei Neizer (O.C. 377), who compares the mitzva of matza to the mitzva of sukka on Sukkot. On the first night of Sukkot, the Torah obligates us to eat bread in the sukka, whereas throughout the rest of Sukkot, the requirement is that if we wish to eat a meal, or sleep, we must do so in the sukka. Likewise, the Avnei Neizer writes, the Torah requires us to eat matza on the first night of Pesach, and throughout the rest of Pesach, the requirement is that if we wish to eat one of the five principal grains, we must eat the grain in its unleavened form. And thus just as we fulfill a mitzva each time we eat in the sukka on Sukkot, even though we are obligated to do so only on the first night, similarly, we fulfill a mitzva each time we eat matza on Pesach, even though we are obligated to do so only on the first night.
In truth, this issue appears to be subject to a debate among the Rishonim. A number of Rishonim raised the question of why we recite a berakha (“lei-shev ba-sukka”) each time we eat in the sukka on Sukkot, even beyond the first night, whereas a berakha over matza (“al akhilat matza”) is recited only the first night of Pesach, at the seder, and not during the rest of Pesach. The Maharil (Hilkhot Sukkot) answers, very simply, that one fulfills a mitzva each time he eats in the sukka throughout Sukkot, which is not the case with matza on Pesach. The clear implication of the Maharil’s comments is that eating matza does not fulfill a mitzva after the first night of Pesach. This answer is given also by Meiri (Sukka 27a), who compares eating matza after the first night to eating kosher meat all year round. Eating kosher meat avoids the prohibition of eating non-kosher meat, but does not fulfill a mitzva; likewise, according to Meiri, eating matza on Pesach (beyond the first night) avoids the prohibition of eating chametz on Pesach, but does not fulfill a mitzva, and so it does not warrant a berakha.
The Ba’al Ha-ma’or (Pesachim 26b in the Rif), however, answers differently. He explains that the seven-day obligation of sukka includes activities that one cannot avoid for seven days – specifically, sleeping. In effect, then, the mitzva of sukka is obligatory even beyond the first night of Sukkot, as one by necessity will need to use the sukka. This “obligatory” quality of sukka renders this mitzva worthy of a berakha, even beyond the first night. On Pesach, however, one can easily subsist on other foods, and does not require matza, and thus eating matza is truly optional after the first night of Pesach. For this reason, the Ba’al Ha-ma’or writes, no berakha is recited when one eats matza beyond the first night.
Significantly, the Ba’al Ha-ma’or accepts the premise that eating matza after the first night of Pesach fundamentally resembles eating in the sukka after the first night of Sukkot. In his view, there is only a practical difference between them – that one can be avoided, while the other cannot, a difference that affects the specific issue of reciting a berakha. It seems clear that the Ba’al Ha-ma’or acknowledged a mitzva to eat matza even beyond the first night of Pesach, just as one fulfills a mitzva by eating and sleeping in the sukka beyond the first night of Sukkot.
(Based on Rav Asher Weiss’ essay on the topic)