Preheat your oven to 150°C / 300°F. Line a 20cm / 8-inch square cake tin with baking paper.
Using an electric or hand-held mixer, cream the butter, caster sugar, and vanilla together until light and fluffy, about 3 to 4 minutes.
Add the cake flour, cornflour, and toasted milk powder. Mix briefly until just combined and the dough holds together. The dough will be quite stiff. Use a spatula to scrape the flour from the sides of the bowl, making sure everything is fully absorbed. The dough is very thick.
Break the dough into pieces and press it evenly into the prepared tin. Use an offset spatula or bench scraper to even out the surface.
Bake for 45 to 50 minutes until lightly and evenly golden across the top. If you prefer a more blonde shortbread, cover loosely cover with foil for the last 15 minutes of baking, and check for your level of doneness from about 30 minutes into the baking time.
About 5 to 10 minutes before the end of the baking time, sprinkle lightly with caster sugar. Or, you can add it as it comes out of the oven.
Remove from the oven. While still warm, use a ruler or tape measure to mark where you want to cut, then slice into fingers using a sharp, unserrated knife.
Allow the shortbread to cool completely in the tin before removing and breaking the fingers along the cut lines. Store in an airtight container at room temperature for up to two weeks.
To make individual round biscuits: Divide the dough into two equal portions. Roll each into a log, wrap tightly in cling film, and refrigerate until firm, at least 1 hour. Line 1 to 2 baking trays with baking paper. Slice rounds off each log and place on the trays with a little space between each. Bake at 150°C / 300°F for 20 to 22 minutes until just golden at the edges. Sprinkle with caster sugar about 5 minutes before the end of baking.