Line a 12-section bun tray with paper cake cases. Cook the potatoes in a saucepan of salted boiling water for 8 minutes or until only just tender. Drain and leave to cool.
Mix the saffron with the boiling water in a jug and leave to stand for 5 minutes. Whisk together the saffron and water, milk, oil and egg with a fork in a bowl.
Mix together the flour, baking powder, chopped thyme and salt in a separate bowl, then stir in the potato. Add the saffron mixture and mix with a large metal spoon until evenly combined.
Divide the mixture between the paper cases. Brush the tops lightly with the egg yolk mixture. Sprinkle with a little extra salt and scatter with thyme sprigs. Bake in a preheated oven, 220°C (425°F), Gas Mark 7, for 15 minutes or until risen and pale golden. Transfer to a wire rack. Serve warm or cold, split and buttered.