Mardi Gras King Cake

Ingredients

• Dough
• ½ cup water
• ½ cup milk
• 6 tablespoons unsalted butter
• 1½ teaspoons pure vanilla extract
• 3 eggs
• 4¾ cups all-purpose flour
• 1 tablespoon instant active yeast
• 1½ teaspoons salt
• ⅓ cup granulated sugar
• ¼ teaspoon nutmeg
• Filling
• One 8-ounce package cream cheese, at room temperature
• 4 tablespoons unsalted butter
• ½ cup light brown sugar
• ¼ cup granulated sugar
• 1 tablespoon cinnamon
• 1 cup pecans, roughly chopped
• 1 tablespoon orange zest
• Icing
• 1½ cups confectioners' sugar
• 3 tablespoons heavy cream, or more as needed
• Yellow, green and purple sprinkles or sanding sugar