Pour the milk and 0,75 dl of water into a large bowl. Dissolve the yeast in the mixture. Add flour, salt and olive oil, and knead into a soft dough. Cover up and proof the dough in a warm place for about 2 hours until it has doubled in size.
Peel the beetroot and dice into 1-2 cm sized pieces. Cut the spring onions with the green stalks into thin rings. Grate the Gruyère AOP coarsely.
Roll out the pastry dough thinly and place in a baking tin covered with baking paper. Season the sour cream with salt and pepper and spread it on the pastry dough. Spread the beetroot, spring onions and Gruyère AOP on top. Pre-heat the oven to 220°C and bake on the lowest shelf for about 15 minutes. Spread the horseradish onto the tart and serve hot.