I'm guessing an old drawer pull. The button and the back-plate are are two different metals. It was manufactured by pouring iron in a mold, with the rivet looking part as a single piece with the main plate. That's what actually passed through a drilled hole in the drawer to attach it.
The decorative button piece is a different metal, pressed (wrapped around) over a nipple used to pull it out of the mold. That button attached the actual pull device, now gone, but was likely fairly heavy itself. Usually too heavy for the metal used to hold it.
The indentations on each side of the large hole held a decorative bumper plate, which the missing pull struck when released. That bumper plate was never physically attached, rather just sandwiched between the backplate and the drawer, held in constant orientation by those indentation on the back.
I'm just guessing, based on design principles I've seen used before, but every indentation, defect, etc., matches that design.