What a great find. Nice collectors item. A.M Peasle/Boston on the back is the button maker. Here's a link to some of his history from wiki: https://en.wikipedia.org/wiki/Aaron_Peasley
Peasley was an engraver and die-sinker from at least 1810 to 1823. According to Albert's Button book it is listed as MS 46B Ancient and Honorable Artillery and dates to 1810. Very nice find.