Mix warm milk, sugar, yeast; rest 5 minutes until foamy.
Add butter, egg, salt, flour; knead 6–8 minutes until smooth.
Cover and let dough rise 45–60 minutes until doubled.
Mix brown sugar, cinnamon, nutmeg, salt.
Roll dough 12×16 inches; spread butter and sprinkle filling.
Roll log; slice 1 inch, then halve pieces.
Place in dish; rise 20 minutes.
Bake 350°F (175°C) for 15–18 minutes.
Whisk powdered sugar, milk, vanilla for glaze.
Drizzle glaze over warm rolls.