How to make
Sift the flour into a bowl and mix it with the dry yeast. Make a hole/well in the middle.
Lightly beat the eggs with the sugar and vanilla. Before that, save a little of the yolk for spreading at the end.
Pour the egg mixture, slightly warmed milk, rum, orange peels and half the butter into the well.
Knead a soft dough, by adding more flour and butter, until you run out, until the dough stops sticking to your fingers. Knead on a floured surface.
Return the dough into the bowl and leave it in a warm place to double in size for about 1-2 hours in a warm room and cover it with a clean towel.
Cover a 11″ (28 cm) diameter baking pan with baking paper. In the middle, place a greased refractory bowl - about 3″ (8 cm) in diameter. Form a ring from the dough (you can also twist two strips from it) and place them in the baking pan. Again leave in a warm place until it rises and doubles in volume.
Spread the risen brioche with the yolk beaten with a little water and oil. Sprinkle generously with sugar mixed with aromatic ouzo or mastic.
Bake at 360°F (180°C) in a preheated oven until golden brown - 30-35 minutes.
Leave brioche to cool completely on a wire rack before slicing and serving it.
The Brioche Ring is ready.