Your goldplated brass 2-piece button with backmark saying "EXTRA RICH W SUPERFINE W" was manufactured during 1838-1846 by the Wadhams & Webster Company of Wolcottville CT. That company is known to have used the term "Superfine" in its button backmarks.
Antique button collectors call your find a "flower-button" from the "Golden Age" of metal buttons. That type of goldplated, very ornate, finely crafted button was made for use on fancy civilian coats and jackets.