Preheat the oven to 180C/200F/Gas 4. Line a baking tray with greaseproof paper.
Cream the butter and sugar together in a bowl until light and fluffy.
Beat in the egg until well combined. Stir in the vanilla and flour until well combined.
Divide the dough into 12 equal pieces and roll each piece into a ball.
Sprinkle the oats onto a plate, roll the balls in the oats and put them on the baking tray. Squash the balls slightly with your hands.
Bake the biscuits for 12–15 minutes, or until pale golden-brown.