Heat the milk so that it is lukewarm, not hot. Pour ½ cup milk into a cup, add a teaspoon of sugar and instant yeast, stir well. Leave in a warm place until small bubbles form on the surface from the activated yeast. This takes about 10-15 minutes. Meantime, melt the butter and let it cool down; it can't be hot.
In a big mixing bowl, place flour, sugar, the rest of lukewarm milk, melted butter, a pinch of salt, and eggs. Add milk with activated yeast.
Make a dough; I'm using my hands and a wooden spoon. Start stirring the ingredients; when combined, knead the dough properly. It requires a bit of physical effort to make the dough smooth and only slightly sticky. It takes about 10 minutes. If the dough is too sticky during processing, add a little flour.
Let the dough rise in a warm place. This works for me: Place a pot with hot water in the bottom of the oven, which is turned off. Put the bowl with kneaded dough on a medium rack. The bowl should not be placed immediately above the pot with hot water, rather somewhere in the corner. Close the oven and let the dough rise for 1 hour. It rises like crazy in this moist and warm environment!
Divide the risen dough into two pieces. Roll out one half of the dough on a flour-dusted worktop roughly into a rectangle shape. The dough should be about as thick as a straw. Using a knife, divide the rolled-out dough into squares/rectangles approximately 4x4 inches in size—place ½ to 1 Tbsp of filling in the middle of each square.
Fold the edges of the dough over the filling and seal well. Finally, gently roll the finished bun between your palms to get a regular shape.
Grease a baking dish about 13x9 inches with butter. Melt ½ stick of butter (60 g) in a saucepan, let it cool a bit. Place the prepared buns one at a time seam-side down in the baking dish, brushing each side with melted but not hot butter.
Make buchty buns in a similar way with the other half of the dough.
Finally, brush the top of the buchty buns with the remaining butter you’ve melted earlier.
Bake in a preheated oven at 320°F (160°C) for about 40-50 minutes, until golden brown.
Melt the rest of the butter intended for brushing (about ¼ stick - 25 g), pour in golden rum, mix. Once the buns are freshly out of the oven, brush the surface with the butter and rum mixture.