For the purposes of this question the builders are incredibly wealthy, have access to cheap nukes to use for excavation, and everyone in this world is immune to radiation.
The technology is decades ahead: but no Clarktech is supposed to be used here, just stuff like lots of nukes, and automation to create the ceramics that line the molds the magma will be made to flow into. So you'd basically be building a larger hollow version of the structure out of, or at least lined with ceramic. Which the magma is injection molded into by its own pressure before the ceramic and any heating elements are finally removed after cooling.
Getting access to a magma chamber from a dormant volcano is possible, but ideally people would just use their plentiful nukes to blast deep enough into the crust that they aren't beholden to the local geology.
This isn't intended to be the most pragmatic method of construction by a long shot, but it seems like by controlling the rate of cooling you could create some truly beautiful buildings injection molded with igneous rock. Plus you could texture it however you want by shaping the ceramic plates of the mold. Though depending on specifics the rock may still need to be polished first anyway (though if the rock didn't touch the air while cooling against a smooth surface maybe it would already be basically polished?).