Pre-heat your oven to 180°c (or 160°c for a fan-assisted oven). Line a couple of trays with some grease-proof paper.
In a large bowl, cream together the butter and sugar.
Add the egg yolk, walnuts and vanilla and mix until combined.
Gradually add the flour and cornflour to the mixture, a little at a time, mixing until it forms a soft dough.
Roll a small amount of dough into balls (between a teaspoon and tablespoon is ideal, depending on how big you want your biscuits to be) and place onto your pre-lined baking trays with a bit of space between them.
Flatten each ball a little with your fingers. Bake for 15 minutes until golden.
Leave on trays until cool enough to touch before transferring to a wire wrack to cool completely.