Preheat oven to 180°C. Grease a 10 inch round loose bottom tart tin with some butter.
To make short crust pastry, mix together flour and butter in a food processor till the mixture resembles breadcrumbs.
Gradually add 2-3 tablespoons chilled water and process till a dough is formed.
Place the dough on a worktop and form into a ball. Wrap in a cling film and refrigerate for 30 minutes.
Meanwhile put the beetroot wedges in a baking dish and drizzle some olive oil on it. Add salt and crushed peppercorns and mix. Place the dish in the preheated oven and roast for 30-40 minutes. Remove from the oven and set aside.
Dust the worktop with some flour, place the dough on it and roll into a ¼ inch thick disc.
Line the tart tin with the disc, place on a baking tray and refrigerate for 30 minutes.
Line the tart base with a butter paper and fill with some kidney beans, put the tin in the preheated oven and blind bake for 20 minutes.
Take out from the oven, remove the beans and paper and bake again for 5 minutes or till the base turns golden brown. Remove from oven and discard the excess crust.
Whisk together eggs, egg yolk, shallot and cream in a bowl. Add salt, crushed peppercorns, parsley and half the feta cheese and mix well.
Spread the mixture evenly in the tart shell, put it back in the oven and bake at 160º C for 20 minutes.
Top with the roasted beetroot wedges and remaining feta cheese, put it back in the oven and bake for 8-10 minutes.