Fresh, Hot Challah

I received a question about whether it is preferable to bake five pounds of flour once every three weeks, thereby fulfilling the mitzvah of hafrashas challah, and serve frozen challah for the subsequent weeks, or to bake fresh challah each week but forgo the mitzvah of hafrashas challah altogether.
Gmail suggested the following automated response:
“Thanks for the email! Regarding the Hafrashas Challah question, I’d lean towards baking a shiur and freezing it. Having fresh challah every week is wonderful, but the mitzvah of Hafrashas Challah is important, and freezing doesn’t diminish the quality too much.”
However, this assumption, that freezing only minimally impacts quality, is debatable. As one friend quipped, Gmail has clearly never tasted fresh challah. In truth, there is often a noticeable difference between fresh and frozen challah.
Let us examine the halachic background.
The Rema (Orach Chaim 242:1) writes that there is a custom to knead a quantity of dough that requires hafrashas challah in order to bake bread for Shabbos and Yom Tov, adding emphatically: one should not deviate from this custom. The Mishnah Berurah explains that this practice serves two purposes: (1) honoring Shabbos through baking, and (2) fulfilling the mitzvah of hafrashas challah on Erev Shabbos.