In a bowl, combine warm milk, yeast, and sugar; let sit until foamy.

In a separate bowl, whisk together flour, salt, and eggs.

Add the yeast mixture to the flour mixture; combine until a dough forms.

Incorporate melted butter and knead until smooth. Let rise until doubled in size.

Preheat the oven to 350°F (175°C).

In a bowl, mix shredded carrots, brown sugar, all-purpose flour (for filling), cinnamon, ginger, nutmeg, cloves, cardamom, and nuts to create the filling.

Roll out the dough into a rectangle, spread the filling evenly, and roll into a log.

Slice the log in half lengthwise and twist together to form a babka shape.

Place in a greased loaf pan and let rise until doubled.

Bake for 45 minutes or until golden brown.

For the drizzle, beat together cream cheese, powdered sugar, and milk until smooth.

Drizzle over the warm babka before serving.