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Put the butter, vanilla and sugar in a big mixing bowl and stir together with a wooden spoon until really smooth. Stir in the ground rice first, then the flour. If it starts to get dry, you might need to use your hands to squish everything together to make a smooth dough.
Put a piece of baking parchment on a baking sheet. Make the dough into a round ball in the middle of the parchment, then use your hands to push it down and flatten it. Get a rolling pin and dust it with some flour so it doesn’t stick to the dough. Use the rolling pin to roll the dough out to a big circle.
Get your 22-23cm round plate, cake tin or cardboard template and place on top of the dough when you’ve rolled it big enough. Use a cutlery knife to trim round the edges to make a neat circle. Use the offcuts to make smaller biscuits or freeze the dough for another time.
Use a knife to mark the giant biscuit into 8 smaller wedge-shaped biscuits – pretend you are cutting a pizza into slices but don't actually cut it. Prick lines from the edge to the centre of the dough. Use the back of a fork to press all around the top of the circle along the edge to make a line pattern (it’s going to be hair for your reindeer!)
Cover with cling film and put the tray in the fridge for 30 mins to get cold. Heat oven to 180C/160C fan/gas 4. Cook the chilled shortbread for 25 mins until golden. Cool completely on the tray, then use a sharp knife to follow the lines you made with a fork and cut into 8 wedges.
Mix the icing sugar with 1-2 tsp of water to make a thickish icing. Dunk each red sweet in and use like glue to stick one on the pointy end of each biscuit to make red noses. Dunk in your white sweets or chocolate buttons and stick them 2cm in from the edge at the other end to be eyes. Use the black writing icing tube to add dots to the white eyes, then let all the icing dry and go hard.
Carefully wrap each biscuit in a square of cellophane or put in a cellophane bag. Twist the middle of a pipe cleaner in a loop around the top of the bag or gathered cellophane to enclose the biscuit. Now twist each end of the pipe cleaner so it looks like the reindeer’s antlers. Add labels and give to your friends and family, or hang on the tree. Will keep for up to 3 days in a cool, dry place.