There are many scholars who have stated that an upright stake was the torture instrument.
The Latin dictionary by Lewis and Short says that crux was a tree, frame, or other wooden instruments of execution, on which criminals were impaled or hanged. In the writings of Livy, a Roman historian of the first century B.C.E., crux means a mere stake. Cross is only a later meaning of crux. A single stake for impalement of a criminal was called in Latin crux sim′plex. One such instrument of torture is illustrated by Justus Lipsius (1547-1606) in his book De cruce libri tres, Antwerp, 1629, p. 19.
There is the book Das Kreuz und die Kreuzigung (The Cross and the Crucifixion), by Hermann Fulda, Breslau, 1878, p. 109, says: Trees were not everywhere available at the places chosen for public execution. So a simple beam was sunk into the ground. On this the outlaws, with hands raised upward and often also with their feet, were bound or nailed....Jesus died on a simple death-stake: In support of this there speak (a) the then customary usage of this means of execution in the Orient, (b) indirectly the history itself of Jesus sufferings and (c) many expressions of the early church fathers. P219-220
Another is Paul Wilhelm Schmidt, a professor at the University of Basel, in his work Die Geschichte Jesu (The History of Jesus), Vol. 2, Tübingen and Leipzig, 1904, pp. 386-394, made a detailed study of the Greek word stau‧ros′. On p. 386 he said: σταυρός [stau‧ros′] means every upright standing pale or tree trunk.
And if you look at the full scripture in Ezra, it is not saying to make a crossbeam, it simply states:
Ezra 6:11 "And by me an order has been put through that, as for anybody that violates this decree, a timber will be pulled out of his house and he will be impaled upon it, and his house will be turned into a public privy on this account.
In this verse, timber is a piece of wood.
Impaled on a timber. That piece of timber is singular...its one stake of timber.