Lawyer's wig (Coprinus comatus)
Pileus dry, white with brown centre, becoming coarse white curved scales; gills white and crowded looking; stipe 10 cm long, 1.5 cm thick, white, smooth and hollow;...
Suburban driveway; very compacted 'Lilydale toppings" (clay with crushed quartzite and granite?) which would seem a difficult 'choice' for any fungi. I can only guess there was something organic buried within the clay.
Also known as 'Shaggy mane' ... (edible).

'Coprinus comatus is a common fungus often seen growing on lawns, along gravel roads and waste areas. The young fruit bodies first appear as white cylinders emerging from the ground, then the bell-shaped caps open out. The caps are white, and covered with scales—this is the origin of the common names of the fungus.