In a saucepan, heat milk to a simmer. Remove from heat and stir in melted butter. Allow mixture to cool to room temperature.
In a large bowl, dissolve yeast in warm water with 1 tablespoon of the sugar. Let stand until frothy, about 10 minutes.
When yeast mixture is bubbling, add cooled milk mixture. Whisk in eggs. Stir in remaining sugar, salt, and nutmeg. Beat in flour, 1 cup at a time, until dough forms.
Turn dough out onto a lightly floured surface and knead until smooth and elastic, about 8 to 10 minutes. Place in a greased bowl, cover, and let rise in a warm place until doubled in size, about 2 hours.
Preheat oven to 375°F (190°C). Punch down dough and divide in half. Roll each half into a rectangle about 10x16 inches.
For the filling, combine brown sugar and cinnamon. Spread softened butter over dough rectangles, then sprinkle with brown sugar mixture.
Roll up each rectangle tightly, starting from a long side. Bring ends together to form an oval. Place on a greased baking sheet. Cover and let rise until doubled in size, about 45 minutes.
Bake in preheated oven until golden brown, about 30 minutes. Allow to cool.
For the icing, combine powdered sugar, lemon juice, and water. Drizzle over cooled cake. Sprinkle with colored sugars.