Ah, that's great. You have what is known as a Trick Coin. They are available in magic and novelty shops for a few US dollars. They look amazing. The coin appears to be two separate coins sliced thin and then glued together, but the outside edge is completely intact. Hey, it's magic!

To make a trick coin you need a milling machine and good machinist skills. Start with the first coin and carefully mill out the center section. This leaves a hollow that is halfway deep into the coin, but completely contained inside the rim. You have a miniature coffee cup with the coin's outside rim in place and a circular hollow inside, ready to be filled with a portion of your second coin.

Now slice the back off your second coin and reduce its diameter so it fits snugly inside the coffee cup. Just a little glue is needed to hold the whole thing together.

Look carefully at the inside of the rim. On one side or the other you will see the seam. Good machinists can make the seam essentially invisible.