In a large bowl, sprinkle the yeast over 1/4 cup warm water, along with a pinch of the sugar. Set it aside for a few minutes, to get foamy. Add the rest of the sugar to the yeast along with the milk, half the butter, egg, flour and salt and stir until the dough comes together. Knead for about 5 minutes, until the dough is smooth and elastic - it should still be quite tacky. (I do this in my stand mixer, with the dough hook.) Put it back in the bowl, cover with a tea towel and let rise for an hour or so, until doubled in size.
Punch the dough down and divide it in half. Roll each out into an 8x12-inch rectangle. Brush all over with melted butter. Cut the rectangle in half lengthwise, then fold each half almost in half lengthwise, leaving about half an inch uncovered.
Cut the dough crosswise in half, then in quarters, making 8 pieces. Arrange in a buttered, greased or parchment-lined 9x13-inch pan in four rows of four, with the long sides of the buns running along the long sides of the pan. (Once you do this once, you'll totally get the hang of it.) Cover with a tea towel and set aside for about half an hour, while you preheat the oven to 350F.
Bake for 20 minutes, or until deep golden. Immediately brush the tops of the buns with the remaining butter while they're still warm - and if you like, sprinkle with coarse salt. Makes 16 buns.