Knead flour, baking powder, egg, sugar, 1 level teaspoon of salt and 100 g butter in flakes in a mixing bowl with the dough hooks of the hand mixer. Then knead with your hands to a smooth dough. Cover and chill for about 30 minutes.
Peel the beetroot and cut it into approx. 3 thick slices. Heat 2 tbsp. oil and 10 g butter in a Tartin pan (28 cm Ø at the top, 23 cm Ø at the bottom), add beetroot and fry over a low heat for about 15 minutes while turning. Deglaze with 2 tbsp vinegar and honey. Season with salt and pepper. Braise for another 5 minutes
Roll out the dough into a circle (approx. 26 cm Ø) on a floured work surface. Prick several times with a fork. Remove the pan from the heat and carefully place the dough on the beetroot. Press the rim lightly. Bake in the preheated oven, 2nd rail from below (electric oven: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for approx. 25 minutes
In the meantime, chop the capers roughly. Wash parsley and mint, shake dry, pluck leaves from the stems and chop finely. Peel garlic and chop finely. Mix herbs, capers and garlic. Stir in 1 tbsp vinegar and 1 tbsp oil, season with salt and pepper. Crumble feta cheese
Take Tarte-Tartin out of the oven, carefully remove from the edge and turn over onto a plate. Sprinkle with feta cheese, add some salsa verde and garnish with mint if desired. Add the remaining Salsa verde