Place 5 tablespoons sugar and milk in a small saucepan, and stir until the sugar is dissolved. Add 55g softened butter, and gently warm the mixture until the butter melts and the mixture is warm but not hot (no warmer than about 40 degrees C). In a large bowl, stir together the yeast with 300g flour until well blended, and pour the milk mixture into the flour-yeast mixture. Stir in 1 beaten egg, and mix until the mixture forms a sticky, wet dough.
Turn the dough out onto a well-floured surface, and knead for about 10 minutes, gradually kneading in 125g of additional flour or as needed to make a smooth, elastic dough. Form the dough into a round ball, place into an oiled bowl, and turn the dough around in the bowl a few times to coat with oil. Cover the bowl with a cloth, and allow dough to rise in a warm place until doubled, about 1 hour.
Cream 55g softened butter with 100g of sugar in a bowl until the mixture is light and fluffy, and stir in dried milk powder, 60g flour, and the coconut until the mixture is smooth and well blended. Set the filling aside.
Working on a floured surface, punch down the dough, and cut into 2 equal pieces. Cut each piece into 8 equal-sized pieces (16 pieces total). Form each piece into an oblong bun, and flatten the bun with a floured rolling pin. Scoop up about 1 tablespoon of filling with a spoon, and place in the centre of a bun. Pull and pinch the edges of the dough together to enclose the filling in the bun. Repeat with all dough pieces, and place the filled buns, seam sides down, onto the prepared baking trays. Cover the buns with a cloth, and allow to rise in a warm place 1 hour.
Preheat an oven to 190 C / Gas 5. Line baking trays with parchment.
For a glossy coating, beat 1 egg in a bowl, and brush each bun with a little beaten egg. Sprinkle each bun with a few sesame seeds.
Bake in the preheated oven until the buns are golden brown, 10 to 15 minutes. Allow to cool before serving.
Recipe makes 16 large buns or 32 small buns.
For bread to rise, warm oven to 70 degrees C. When oven is warm, turn it off and place the covered dough into the oven for 1 hour to rise.