Warm the Milk and Butter: In a small saucepan, heat the milk and butter over low heat until warm (not boiling). Remove from heat and sprinkle the yeast over it. Let sit for 5 minutes until frothy.

Mix the Dry Ingredients: In a large bowl, whisk together flour, sugar, cinnamon, ginger, cardamom, nutmeg, and salt.

Combine and Form a Dough: Add the yeast mixture and the egg to the flour mixture. Stir until a dough forms and knead for 5-7 minutes until smooth and elastic.

Let the Dough Rise: Place the dough in a greased bowl, cover with a towel, and let rise in a warm place for 1 hour or until doubled.

Preheat the Oven: Preheat your oven to 375°F (190°C).

Roll Out the Dough: Punch down the dough and roll it out on a floured surface into a rectangle. Brush with melted butter and sprinkle with a cinnamon-sugar mixture.

Shape the Rolls: Roll the dough tightly from one long side and slice into even pieces. Place cut-side up in a greased baking dish.

Bake the Rolls: Bake for 20-25 minutes until golden brown.

Make the Frosting: In a bowl, whisk powdered sugar, milk, and vanilla extract until smooth. Drizzle over warm rolls.