The Basalt Blade is a trophy from killing a Basalt Golem. Not sure of the drop rate since got mine from the first kill. :)

Basalt Golems can be find in Direlands. Found one with friend not too far from Outside Acursed Halls. Be prepare to take out some Obsidian Golems as well as the Basalt Golem. Friend also found a pyreal nugget (might be 4 motes) in addition to the blade.

You can turn the blade into and axe by giving it to a Trophy Collector.