Mix 500 g flour, 1 pinch of salt, vanilla sugar and sugar in a bowl. Add 1 egg and 75 g butter in pieces. Warm the milk in a small pot lukewarm, crumble yeast into it and dissolve it while stirring. Pour on the flour mixture and knead it with the dough hooks of the mixer to a smooth dough. Cover and allow to rise for about 4 minutes.
Melt 100 g butter in a small pot. Mix brown sugar and cinnamon. Knead the dough on some flour and roll out to a square (approx. 37 x 37cm). Spread the dough with melted butter and sprinkle with cinnamon sugar. Fold the dough square diagonally into a triangle.
Lift the dough triangle onto a baking tray lined with baking paper (approx. 35 x 40cm). Cut approx. 10 cm at the bottom side at a height of approx. 5 cm on both sides towards the middle and fold over. Press the fir tree shape evenly with your hands and cut in several times. Twist "fir branches" slightly.
Whisk the rest of the egg and brush the tree with it. Cover and leave to rise for about 15 minutes. Bake in the preheated oven (electric cooker: 200°C/ convection oven 175°C/ gas: see manufacturer) for 20-25 minutes.