How did Judaism develop in southwest Asia?

Answer 1

Judaism formed in Israel when Abraham formed a covenant with God.

Answer 2

By Abraham in the Middle East.
Tradition states that Abraham founded Judaism. The Kuzari (Rabbi Judah HaLevi, 1075-1141) states that Abraham was gifted with high intelligence; and, as Maimonides (1135-1204) describes, Abraham didn't blindly accept the ubiquitous idolatry. The whole populace had been duped, but the young Abraham contemplated the matter relentlessly, finally arriving at the conclusion that there is One God and that this should be taught to others as well. This is what is meant by his "calling out in the name of the Lord" (Genesis ch.12). As a young man, he remonstrated with passersby in public, demonstrating to them the falsehood of their idols; and our tradition tells how he was threatened and endangered by Nimrod.
Subsequently, Terah relocated to Harran; and it is here that Abraham began to develop a circle of disciples (Rashi commentary, on Genesis 12:5). Later, God told Abraham in prophecy to move to the Holy Land, which is where he raised his family. He continued his contemplations, eventually arriving at the attitudes and forms of behavior which God later incorporated into the Torah given to Moses.
Moses achieved the highest level of prophecy (Deuteronomy ch.34) and was called upon by God (Exodus ch.3). He brought the Israelites out of Egyptian slavery (Exodus ch.12). He received the Torah from God (Exodus 24:12) and later recorded it in writing (Deuteronomy 31:24).
All of the above places are in the ancient Fertile Crescent.

Answer 2

According to our tradition, Abraham (18th century BCE) developed the religion which became known as Judaism. The Kuzari (Rabbi Judah HaLevi, 1075-1141) states that Abraham was a gifted man of high intelligence; and, as Maimonides (1135-1204) describes, Abraham didn't blindly accept the ubiquitous idolatry which had been foisted upon his countrymen. He contemplated the matter relentlessly, finally arriving at the conclusion that there is One God and that this should be taught to others as well. This is what is meant by his "calling out in the name of the Lord" (Genesis ch.12). He continued his contemplations, eventually arriving at the forms of behavior which God later incorporated into the Torah given to Moses. Abraham taught disciples (Talmud, Yoma 28b), gave tithes (Genesis ch.14), strove to raise a family (Genesis ch.15, 17, and 24) which would serve God, made a covenant with God (Genesis ch.15 and 17), welcomed guests into his home (Genesis ch.18) unlike the inhospitable Sodomites (Genesis ch.19), prayed for people (Genesis ch.18), rebuked others when necessary (Genesis ch.20), eulogized and buried the deceased (Genesis ch.23), and fulfilled God's will unquestioningly (Genesis ch.22).

It is therefore clear why God expresses His love for Abraham (Isaiah 41:8) and calls Himself the God of Abraham (Genesis 26:24), and says that Abraham obeyed Him fully (Genesis 26:5).