The idea is to melt the fine-grain portion of basalt regolith using a large Fresnel lens, and let it cool to a solid. The lens would track along a tamped bed of material leaving a molten puddle something like 2 cm thick. This would be done on top of more regolith with the same characteristics - which means some of the material would sink into the stuff below and get mixed. Then it is left to cool to a solid.
The conjecture is that Fresnel lenses, and the equipment needed to create flat beds of tamped powder regolith and track such lenses across it, is so light that it could be a good way of creating construction materials. If they aren't very good materials they could make up for that in the simplicity of making them and the possibility of making enough that the fact they have weaknesses doesn't matter - just use more.
What might the material yielded by such a process be like?
Edit: Since someone asked, this could yield thin basalt objects of any 2D shape, or objects built up of various layers into 3D shapes. Such objects can be joined with more molten basalt and parged to form continuous rock walls, floors, and arches. An approach to excavation also based largely on the use of lenses (for trenching, and boring for the placement of explosive micro-charges) is used to create voids that are then lined with rock this way.
It is explained more here, and here is the current model of the equipment: