Amethyst geodes in Minecraft are covered with unique blocks, which you will find only there. Smooth basalt is one of those blocks that multiply naturally around it. A thick outer layer surrounding calcite, a white layer and dark purple amethyst, which contains the starting blocks that form amethyst clusters with amethyst shards, and regular amethyst.
In addition to finding smooth basalt surrounding amethyst geodes, you can also do so. All you have to do is find regular basalt blocks, bring them to the furnace, have the fuel ready, and melt them. Your basalt block will turn into smooth basalt and should have a slightly altered appearance.
Of the two options, finding basalt will be easier than finding smooth basalt in the wild. You will only find it around amethyst geodes and these are quite rare. The amethyst geode usually occurs between Y = 70 and the subsoil. Regular basalt blocks regularly appear in the underworld. If you have access to the underworld, you have a better chance of finding it there quite often, but if not, you may want to test your chances of finding amethyst geodes on your travels.
Once you have your smooth basalt, it is mainly used for decoration. Not required for any craft recipes.