The torah and other Jewish literature make clear that "challah" is a catch all that describes a normal bread that is often used in offerings, or portions of it are given as sacrifices or as gifts. Although the Bible doesn't usually physically describe the appearance of what normal bread is, we know it's a type of flatbread from various proofs.
One proof is we know ancient Israelite ovens (tanur) are designed for flatbreads.
The Persians introduced a clay oven called a tanur (similar to the Indian tandoor), which had an opening at the bottom for the fire, and through which the bread was placed to be baked on the inner wall of the upper chamber from the heat of the oven and ashes after the flames had died down. This continued to be the way in which Yemenite Jews baked bread until modern times. The remains of clay ovens and fragments of bread trays have been found in several archaeological excavations.
All these methods produced only thin loaves, and the custom was thus to break bread rather than cut it. The bread was soft and pliable and used for dipping and sopping up gravies and juices.
Another of is because you can have matzot that are called challot.
26 And out of the basket of unleavened bread, that was before the LORD, he took one unleavened cake, and one cake of oiled bread, and one wafer, and placed them on the fat, and upon the right thigh.
כו וּמִסַּל הַמַּצּוֹת אֲשֶׁר לִפְנֵי יְהוָה, לָקַח חַלַּת מַצָּה אַחַת וְחַלַּת לֶחֶם שֶׁמֶן אַחַת--וְרָקִיק אֶחָד; וַיָּשֶׂם, עַל-הַחֲלָבִים, וְעַל, שׁוֹק הַיָּמִין.
Another proof is supposedly the earliest source of Hallah as a "Shabbat bread" says the following:
15th c. German work Leket Yosher (p. 49) as referenced by John Cooper’s Eat and Be Satisfied: A Social History of Jewish Food
I remember that on every Friday afternoon they would make three thin ḥallot that were kneaded with eggs, oil, and a little bit of water. In the evening, since the table was square, the middle ḥallah was put in the middle of the table on the middle tablecloth. Under the ḥallah was a large whole loafâ€¦In the morning the large ḥallah and a large loaf were put on the table like in the evening. For the third meal the small ḥallah and a small bread was taken.
According to a different answer on Mi Yodeya, not only does the braided aspect of challah not come from a Jewish source, but seems to have direct ties to outright paganism and idolatry.
the potential origin recorded by Menachem Mendel:
I mentioned this to my colleague Rabbi Jill Hammer, and she suggested that I look into the connection between ḥallah and goddess
worship. Not really knowing what to expect, I found the following in The Woman’s Dictionary of Symbols and Sacred Objects (p. 482):
The braided bread loaves of Germanic tradition were invented by the women of Teutonic tribes, who used to make offerings of their own
hair to their Goddess. Eventually they learned to preserve their braids by substituting the imitative loaf, which was called Berchisbrod or Perchisbrod, bread offered to the Goddess Berchta, or Perchta. The name of the braided Sabbath loaf among German Jews, Berches or Barches, was copied from this tradition.
Could it be that those nice braids that my wife makes when she bakes ḥallah really have their source in pagan goddess worship? The
linguist Paul Wexler thinks that the original name was actually the German Holle which was the name of a pagan Germanic goddess to whom braided bread was once given in offering. [The German] Holle was replaced at a later date-under the pressure of Judaization-by the [Hebrew] ḥallah, which bore formal and semantic similarity. (See his book The Non-Jewish Origins of the Sephardic Jews, pp. 68-69 and numerous other places in his writings.)
Along the same lines:
Joshua Trachtenberg, in his book, Jewish Magic and Superstition, claims that Ashkenazic Jews in German lands as early as the 10th
century adopted the practice of braiding their ritual loaves from their neighbors who worshipped the goddess/spirit Perchta, or Holda, or Holle. According to Trachtenberg, these German women worshiped the goddess by offering their braided hair! The tradition of the times was braiding loaves of bread, called Perchisbrod, as an acknowledgement of this pagan custom.
So my question is, how can something seemingly so disconnected from Jewish tradition, with credible links to pagan origins, become a "symbol" of "Judaism/Jewish Practice?"