Wash the orange hot, rub dry and finely grate the peel. Halve the orange and squeeze the juice. Measure out 50 ml of juice. Use the rest of the juice for other purposes. Grease a springform pan (26 cm Ø) and sprinkle with flour.
Mix flour, baking powder and orange peel. Separate the eggs. Whisk egg yolks, salt and 75 g sugar with the whisk of the hand mixer until thick and creamy. Slowly allow the olive oil to run in while stirring.
Stir in the flour mixture briefly. Beat the egg white in 2 portions until stiff, adding a total of 75 g sugar. Fold the egg whites into the dough in portions.
Pour into the springform pan, smooth it down and bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for 25-30 minutes. Open the oven door and let it rest in the switched off oven for about 15 minutes.
Meanwhile, put 100 g sugar, cognac, 50 ml water and measured orange juice in a pot, bring to the boil and simmer over a low to medium heat for about 5 minutes. Remove from the stove and let it cool down.
Take the cake out of the oven and remove from the edge of the springform pan. Place the cake on a cake rack, sprinkle with the cooled syrup and let it cool down. Remove from the springform pan. Dust the rim with icing sugar.
Cut cake into 12 pieces and arrange on a plate. Serve with Greek yoghurt and honey, possibly decorated with thyme.