prepare the base dough
Prepare the yeasted dough. Add the all purpose flour, yogurt, milk, sugar, yeast and salt into the bowl of a stand mixer. Place the bowl onto the stand mixer, attached with the dough hook, and mix until dough forms, for about 5 minutes. Gradually add in the soft butter in small sized chunks. Once the butter has been incorporated mix for another 5 minutes on medium speed. Cover with cling film and leave to proof at room temperature for 1 hour or until dough has doubled in size.
prepare the millet filling
In a small saucepan over medium low heat cook the millet, pinch of salt, sugar, butter and vanilla beans from the pod until the millet is completely cooked, stir occasionally. Remove from the heat and let it cool completely.
prove the dough
Lay the baking paper on a large baking sheet. Place the dough in the middle. With lightly floured hands, flatten the dough, pushing it from the middle to the outside (like you would be making pizza) until you have an even thickness of 3 mm / 1/8 ″ and a raised rim of about 2 cm / 25/32 ″. Pour the millet filling into the yeasted case. Cover with a cling film and leave to prove at room temperature for 40 - 60 minutes. Preheat the oven to 210 degrees C / 410 degrees F.
bake and serve
Brush the trim with an egg wash and sprinkle with pearl sugar. Bake for 30 minutes at 190 degrees C / 375 degrees F. Meantime prepare the sour cream topping. In a small bowl combine together the egg yolk, sugar, sour cream, yogurt and heavy cream. Remove the Millet cake from the oven, pour the topping over the filling and place back into the oven. Bake for another 20 minutes. Serve warm.