I am recently retired from the luxury leather good industry but I am still consultant for several companies in Europe.
My formal company was working for Hermes, Louis Vuitton, Chanel... and was making most of the metallic accessories that you may found on luxury bags, pens, jewellry....
I never had a badge in hand to inspect it, but from the photos I saw, the process to produce the badge should be similar to the one use to produce belt buckles or other decorative plate that you may found on luxury leather bags.
The technic is simple but require a little bit of skill. First you have to stamp or cnc machine the part in metal, brass plus plating is possible but the simpliest is SST. You have to create the borders of the shapes to color by making some "pockets" in the metal with a depth of at least 0.3mm or 0.015 inch.
Then those recesses are bead blasted to facilitate the adhesion. To color them, you use liquid lacquer like epoxy or acrylic that you apply to fill the recess with a seringe. Then the lacquer is cooked in an oven about 160°c for 30mn. I simplify for the explanation, but there is plenty of tricks to get a godd adhesion and avoid to have bubles inside.
Then there is two cases :
- you just leave the part as is and it is finished, you may add a light polishing for brightness, in this case the laquer will appear with a concave meniscus
- or you grind the metal and the laquer in the same time and polish the part to put everything on the same level. At the end, the laquer will appear like the photo of the Hermes buckles. If brass is use as the base material the plating needs to be done after ther laquer and grinding process.
The is an expensive technology because everything is manually done, but in France or Italy several companies (small and big) may handle it, even from scratch if a drawing may be supplied for creating the metallic base.