Preheat oven to 200C (390F) fanbake. Lined a 12 hole muffin pan with a little square of baking paper in the bottom of each hole, and lightly brush each hole with olive oil.
Grate the potatoes onto a clean tea towel, then use the tea towel to wring out all the excess moisture over your kitchen sink. Quite a surprising amount of liquid will be released. Tip the grated potato into a mixing bowl and sprinkle over the rice flour, salt and a good grind of black pepper. Stir to coat everything evenly, then press the potato mixture evenly into the greased muffin pan. Make a little depression in the middle of each - all the better to hold the aioli which will come later.
Bake for 20-25 minutes, until golden brown and crisp. Remove from the oven and pop each potato nest out onto a serving platter.
Top each potato nest with about 1 tsp of eggless aioli (or aioli/mayonnaise of your choice), and matchsticks of beetroot, radish and apple. Sprinkle freshly grated lemon zest over the top, and garnish with a sprig of fresh thyme.
Serve immediately, with a glass of your favourite tipple.