Preheat the oven to 180°C.
In each of 6 blini or 10cm-diameter pans, place 3 onion halves, 30ml onion juice and 3 red and 3 gold pieces of beetroot. Bring to the boil over moderate heat and simmer to reduce the liquid by half. Remove from the heat, place a pastry round on top of the mixture in each pan and using a teaspoon dusted in flour, pat the sides down around the edges, almost like an upside-down pie. Place in the oven and bake for 25 minutes. Remove from the oven and turn onto serving plates. Garnish each tart with 1½ tablespoons of feta, a sprinkle of pine nuts and 2 pea tendrils.
Wash the beetroot and trim the roots and tops. Place in a saucepan, cover with cold salted water, bring to a simmer and cook until tender (about 10–12 minutes). Drain, cover with fresh cold water and leave to cool. When cool, rub the skins off while submerged under water. Slice each into 6 wedges and drizzle liberally with the caramelised balsamic vinegar.
Sift the flour and salt into a large bowl. Add the butter to the bowl and rub it in loosely (small chunks of butter should be visible). Make a well in the flour, pour in the water, then mix to a firm, rough dough. Cover with plastic wrap and rest the dough for 20 minutes in the refrigerator. Turn out onto a lightly floured surface, knead gently and form into a smooth rectangle. Roll the dough, in one direction only, until its length is 3 times its width, about 20 x 50cm. Keep edges straight and even. Don’t overwork the butter streaks; you should have a marbled effect. Fold into thirds. Give the dough a quarter turn and roll out again to 3 times its width. Fold as before, cover with plastic wrap and chill for at least 20 minutes. On a lightly floured surface roll out the pastry to a thickness of 5mm then cut out 6 x 10cm discs. Set aside until needed.