It looks like a one piece button to me. Please post a picture of the other side. Leavenworth, Hayden and Scovill were in business from 1811-1827and that was before two piece buttons were introduced. Also, I am pretty sure the wording at the top of the button reads "Treble Gilt" which means it would have been gold plated.
From looking around it must have been a civilian button with a smooth front .
Still can't find an example pic of a button with the L,H &S on it . Still happy as I don't find many buttons .