Heat the milk until lukewarm and dissolve 1 tsp of sugar. Add in the yeast (swirl the cup gently to dissolve) and keep closed for 10-15 min until frothy. This step is done to proof the yeast.
Take the flour is a large bowl. Add in the remaining sugar (3 tsp), salt and mix well. Make a dent in the middle, add the milk-yeast mixture, melted butter, a whisked egg, warm water and knead well (6-10 min) until you get a smooth, pliable dough. If the dough is too dry add in a few tsp of water or if it is sticky, add in more flour. Wrap the bowl with cling wrap or a tea towel. Leave in a warm place to rise for about 1 hour.
While the dough is rising, boil the potatoes, peel the skin and coarsely mash. Keep aside for later. Heat oil/ghee in a skillet and add in the mustard seeds, urad dal, curry leaves and a pinch of asafoetida. Fry till the urad dal turns golden brown and the curry leaves are crisp. Now add in the onions, chopped green chillies, minced ginger and fry till onions turn translucent. Add in a pinch of turmeric and then the boiled potatoes, salt to taste and lime juice. Turn off the heat. Garnish generously with chopped coriander leaves. Check the seasoning and keep aside to cool.
At the end of the hour, you will notice that the dough has doubled in volume. Punch the dough down and knead it again. Shape the dough into a log and cut into 8 even pieces. Shape them into balls. You can weigh the dough balls if you are very particular about the uniformity in size.
Flatten the dough balls with the palm of your hand or a rolling pin and add a lime sized ball of the filling in the centre of it. Pinch the edges of the dough to cover the filling. Make sure there are no gaps. Reshape the dough ball with your hands into a ball.
Place a sheet of parchment paper/aluminum foil over a baking tray. Place the buns on it leaving some distance between them. Leave to raise for another 20 min. While this is going on, preheat the oven to 190 deg C. Brush the raised buns with the whisked egg white and sprinkle white sesame seeds over the surface. (Alternatively, you could brush the buns with milk and then sprinkle the sesame seeds on top).
Bake (on level 3 of the oven) for about 20 min until the buns turn golden brown. Once done, immediately brush them with melted butter. Serve hot with chutney/sauce of your choice.