Another addition for me is this 1836 Bustie. A beautiful coin in my eyes. A total of 6,545,000 were minted and she does have the edge lettering.
I was admiring your coin's nice strike (Stars, E Pluribus Unum, etc), when I recalled that the Thonnelier steam coin press was first put into operation in March of that year in Philadelphia. I wonder if 1836 halves were pressed by both the old and new presses and, if so, how easy it is to tell the difference.
Robert Maskell Patterson, the director of the Mint from 1835 to 1851, wrote the following report to President Andrew Jackson in 1837: "On the 23rd of March last (1836), the first steam coinage in America was executed at this Mint; and the performance of the press, in which the power of the lever is substituted for that of the screw, has answered all our expectations. Since that time, all the copper coins have been struck by this press, and it has been lately used with success for coining half dollars. The workmen are now engaged in making other steam presses; and as these are completed, the coining by human labor be abandoned, and the work that can be executed in...the Mint will be greatly increased." https://www.fi.edu/history-resources/coin-press It sounds like it was 1837 when they swapped presses for the Half Dollar.
Actually, the approximately 1200 1836 reeded edge bust halves were struck in November of 1836 on the mint's first steam press.
Is there a way to tell them apart? It the OP's coin is one of the 1200...that would really be something!
One way to tell them apart is that the newer design has a reeded edge rather than letters (thus the name). But the easiest way--especially with slabbed coins where the edge view is less than desirable is that the reverse is quite a bit different. 1836 LE reverse 37 RE (since I don't own a '36 RE)
My bad, I see now. I was thinking they swapped the same dies between the two machines and the only way to tell was by strike quality. (never mind)