Heat the oven to 325°F. Line a 9-by-13-inch metal pan with parchment, leaving enough overhang to lift out the baked shortbread.
Beat butter and 1/2 cup sugar for 1 minute until smooth, without whipping in much air. Mix in vanilla, then flour, cornstarch and salt until crumbly clumps form.
Press the dough evenly into the pan. Prick all over with a fork, mark 24 fingers lightly with a knife and scatter the tablespoon sugar over the top.
Bake for 30 to 35 minutes, until the surface looks dry and the edges are pale gold. Let stand for 5 minutes, then recut along the marks while still warm.
Cool completely in the pan before lifting with the parchment and separating the fingers.