Reisfladen (Rice Pudding Cake)

Combine 1/2 gallon milk, rice, and sugar in a slow cooker. Cook on High until rice is puffy but mixture is still thin, about 3 hours 15 minutes.

Mix 3 eggs, 1/4 cup milk, vanilla extract, and salt together in a bowl. Add 1/2 cup of the hot rice mixture, stirring in 1 tablespoon at a time, until blended. Pour mixture into the slow cooker, stirring constantly. Cook on Low until rice has absorbed all the liquid, about 30 minutes more. Let cool to room temperature, about 2 hours.

Meanwhile, place flour, yeast, sugars, egg, lukewarm milk, and melted butter in a bread machine in the order listed. Run Dough cycle. Remove dough from the machine after the cycle is done, about 90 minutes. Let rise in a warm place until doubled in volume, about 30 minutes.

Preheat the oven to 400 degrees F (200 degrees C). Butter an 11-inch springform pan. Smooth dough into the pan.

Whisk 2 eggs and brush all but 1 tablespoon onto the dough. Pour rice pudding onto the dough and brush top with remaining egg wash.

Bake in the preheated oven until a toothpick inserted into the cake layer comes out clean, about 25 minutes. Let cool for 5 minutes and release cake from the pan. Let cool completely. Refrigerate until thoroughly chilled, 6 hours to overnight.