In a mixing bowl, combine warm milk, sugar, and yeast. Let it sit for 5 minutes until frothy.

Add melted butter, egg, salt, and flour. Mix until a dough forms.

Knead the dough on a floured surface for about 5 minutes until smooth. Place in a greased bowl and cover with a towel. Let rise for 1 hour.

In a bowl, mix grated carrots, brown sugar, cinnamon, and chopped walnuts.

Preheat the oven to 350°F (175°C). Roll out the dough into a rectangle on a floured surface.

Spread the filling evenly over the dough, then roll it tightly into a log.

Cut the log into 8 equal pieces and place them in a greased baking dish. Let them rise for another 30 minutes.

Bake the rolls for 25 minutes or until golden brown.

While baking, prepare the frosting by mixing cream cheese, butter, powdered sugar, and vanilla until smooth.

Once the rolls are done, let them cool slightly before spreading the frosting on top.