In a large bowl, stir together milk, 1 tablespoon of the brown sugar and yeast.

Let sit at room temperature until foamy, about 5 minutes.

Meanwhile, in a large bowl, whisk together flours, 1 teaspoon of the cinnamon, 1 teaspoon of the salt and nutmeg.

Shape dough into a ball.

Lightly butter a large, clean bowl and place dough in the bowl.

Cover with plastic wrap and let sit in a warm spot until doubled in size, about 1 1/2 hours.

Meanwhile, combine carrots, walnuts and remaining 4 tablespoons butter, 1 teaspoon cinnamon and 1/4 teaspoon salt in a food processor and pulse until finely chopped into a coarse paste, scraping down sides of food processor bowl and stirring often.

Transfer to a bowl and stir in raisins. Lightly butter two 8x4-inch or 9x5-inch loaf pans.

In a small bowl, whisk together remaining egg and 1 tablespoon water to make an egg wash.

Using a closed fist, punch down dough and divide into 2 equal pieces.

On a floured surface, roll out 1 piece of dough into a 12x16-inch rectangle.

Leaving a 1-inch border around outside edge, spread with half of the carrot mixture and sprinkle with 1/4 cup of the brown sugar.

Brush edge with egg wash.

Starting with a long side, snugly roll up dough to form a log with the final seam on the bottom.

Shape log into a "U" and then gently twist the 2 sides together to form a figure eight.

Brush ends with egg wash and pinch together to seal.

Carefully place in a prepared pan.

Repeat with remaining dough, carrot mixture and 1/4 cup brown sugar.

Brush tops of loaves with egg wash, cover loosely with plastic wrap and let sit in a warm spot until puffed and risen well above the pan, about 1 hour.

Preheat the oven to 350F.

Gently uncover loaves and bake until very deep golden brown and cooked through, about 1 hour.

Let cool in the pans on a wire rack for 15 minutes, then gently remove loaves from the pans and cool completely on the rack.

To make the icing, if using, combine cheese, powdered sugar, milk and salt in a bowl and beat with an electric mixer on medium speed until smooth.

Spread onto cooled loaves.