Combine the water and milk in a medium saucepan and warm over low heat until it is about 37°C. Remove from heat and sprinkle the yeast over the surface over the liquid. Sprinkle a pinch of the sugar over the top and set aside without stirring, until foamy, about 5 minutes.
Whisk the butter, egg yolk and vanilla into the yeast mixture.
Whisk the flour, the sugar, salt and nutmeg in a large bowl. Make a well in the center of the flour and stir in the yeast mixture with a wooden spoon to make a thick and slightly sticky dough. Turn dough onto a floured work surface and knead until soft and elastic, about 6 minutes. Shape into a ball.
Note: If you're using a food processor, attach the dough blade at stage three, add all the ingredients and pulse until the dough comes together in a ball.
Brush the inside of a large bowl with butter. Put dough in the buttered bowl, turning to coat lightly with butter. Cover bowl with plastic wrap, trace a circle the size of the dough on the plastic, and note the time. Let rise at room temperature until doubled in size, about 1 hour 15 minutes.
Turn dough out of the bowl and knead briefly to release excess air; reform into a ball and return to the bowl. Lightly butter a large piece of plastic wrap and lay it on the dough. Cover the entire bowl tightly with plastic and proof in the refrigerator for 4 hours or overnight.
To fill and form the rolls: Butter a 9-by-13-inch baking pan. Whisk the sugar and cinnamon together in a small bowl. Turn prepared dough onto a floured work surface and press, then roll into 10-by-18-inch rectangle, with a long edge facing you. Spread the softened butter evenly over the surface of the dough, leaving about an inch border on the side opposite you. Evenly scatter the cinnamon-sugar over the butter. Starting from the long side facing you, roll the dough up into a tight cylinder. Lightly brush the clean edge of the dough with water. Press the open long edge to the dough to seal the cylinder.Slip a long taut piece of string or dental floss under the roll, about 1 1/2 inches from the end. Lift and cross the string ends over the roll, then pull the ends tightly in opposite directions to cut a single roll. Repeat, cutting every 1 1/2 inches, to make 12 rolls. Place the rolls cut-side-down in the prepared pan, leaving 1 inch of space between them. Cover the rolls loosely with plastic wrap. Set aside in a warm place to rise until rolls double in size, about 1 hour 10 minutes. Position the rack in the center of the oven and preheat to 175°C. Bake buns until golden brown and the tops of the buns spring back when pressed lightly, about 30 minutes. Cool in the pan for 10 minutes. To make the glaze: Sift the confectioners' sugar into a medium bowl. Whisk in the condensed milk, butter, and lemon juice to make a smooth, slightly loose icing. Add the vanilla and cinnamon. Drizzle the icing over warm buns. Serve. *Cook's Note: These may be refrigerated or frozen after forming. If refrigerated overnight, allow buns to come to room temperature for about 1/2 hour, then proof fully (until doubled in size) before baking, about 2 hours. If frozen, allow buns to come to room temperature, about 1 hour, and then proof fully (until doubled in size) before baking, about 2 hours. Storage: Though the buns are best eaten on the day they are baked, they will keep, covered, for a day. They freeze well.