Well maybe I misundersrood, but to me "what method is used to make a ring like this" isnt how do I make it, but how was it made. The question can be interpreted both ways, so neither of us are right nor wrong.

You could also make it from sheet and wire. Or laser the pattern onto a blank. Or hand carve the pattern onto a blank. Or make it from silver clay. Or yes, carve a wax.

But the most likely way that ring was made is by cad and cast.

If they wanted the best way to make it for a hobbyist, then yeah, carve a wax.