Warm the milk in a medium saucepan over low heat until it reaches about 100 degrees F. Remove from heat and sprinkle yeast and 1/4 tsp sugar on top. (Don't stir it in.) Set aside until foamy, about 5 minutes. Whisk in the melted butter, egg yolk, and vanilla.

In the bowl of a countertop mixer with the dough hook attached, add the flour, remaining 1/4 cup sugar, salt, and nutmeg. Stir until combined. Make a well in the center and pour in the yeast mixture. Mix on low speed until thick and slightly sticky. Increase to medium speed and mix for 6 minutes, or until dough gathers around the hook.

Remove the dough and shape into a large ball. Lightly butter the mixing bowl, and return the dough to the bowl, turning to coat with butter. Cover with plastic wrap and let rise in a warm place until doubled in size, about 1 hour 15 minutes.

Turn the dough out onto a lightly-floured countertop, and roll the dough into a 12x14-inch rectangle with the longer side facing you.

Spread the softened (not melted!) butter evenly across the top of the dough, leaving a 1/2-inch border on the far long edge. Combine the cinnamon and sugar, and sprinkle evenly over the butter.

Brush the unbuttered far edge with water. Roll the dough away from you into a tight cylinder and pinch along the long edge to seal.

Cut the cylinder with a sharp knife into 6 equal-sized buns. Gently shape the rolls into rounds and place on a well-buttered sheet pan, leaving space between each bun. Cover and let rise in a warm place until doubled, about 40 minutes. Preheat oven to 325 degrees F.

Bake the buns until golden brown, about 35 minutes. Allow them to cool in the pan for 15 minutes.

While the buns are cooling, make the glaze by sifting the confectioner's sugar into a bowl. Whisk in the cream and melted butter.

Transfer the buns onto a cookie rack and spoon the glaze on top while still warm.