If you do not require the thickness apparent in the provided image, you may be satisfied with laser foil, also called heat transfer foil. The laser aspect is somewhat misleading, as it uses a laser printer (or toner-based copier) to bond the foil to the paper.
The base concept in the above described process is that toner is printed in the normal manner on paper or card stock. The laser transfer foil is then attached to the surface to cover the printed area. The layers are then fed through the printer, printing nothing on the second pass. The fusing drum heats the pre-printed portion, causing the foil to merge with it. When cooled (seconds later), the foil is removed except for the melted segments.
Using the same foil, one can perform similar results with a laser engraver/cutter.
If you are not considering high production levels, an inexpensive monochrome laser printer and rolls of the foil may do as you require. The thickness of the cardboard has to be minimized to no more than the maximum capacity of the printer.
The debossing (opposite of embossing) portion would complicate matters, although manual stamping after the foil is applied may work. I don't believe that a laser printer will perform well in areas of paper that has become recessed due to debossing, which would prevent the laser foil from bonding.
As you can see in the above photo, the material can be applied to a wood surface. It's unlikely that the wood was run through a laser printer prior to the foil application!