Lechem Mishneh: Sod ha-Shabbat
We read in the Talmud (Berachot 39b, Shabbat 117b): Rabbi Abba said, “On Shabbat one is obligated to break bread over two loaves, as it is said, “They gathered twice as much bread.” (Exodus 16:22) Rabbi Ashi said, “I saw that Rabbi Kahana held two loaves but broke bread over one.”
“Twice as much bread,” the two loaves correspond to “Remember” and “Keep.”
These two symbolize the union of Tiferet and Malchut: The extra loaf alludes to the added spirituality of Shabbat exemplified by the Neshama Yeteirah.
But why two Omers? An Omer is 1/10th of an Ephah (Exodus 16:36) making 2/10ths of an Ephah for each loaf. But since the two tenths, Shechina and Tiferet, unite on Shabbat, the Children of Israel gathered “two omers for one.” For this reason, we break over two loaves on Shabbat indicating that they are really one entity, one essence. (Otzar HaKavod)
The two challot should be joined together in our hands, as it is written, “You shall keep My Shabbats (plural).” Ateret Tiferet – Malchut and Tiferet, and the two become one.
The two loaves should be held by the ten fingers to unite all ten Sefirot. (Sefer Qanah 65b)
I received a tradition that “but broke bread over one,” is a reference to the bottom loaf.
Rabbi Todros ha-Levi, may his memory be for a blessing, explained this custom in accord with the verse, “No one can see My face, for no man shall see Me and live.” (Exodus 33:20)