In a bowl, combine warm milk, yeast, and sugar. Once the mixture becomes foamy, gradually mix in the flour and salt. Knead the dough into a smooth ball. Cover and allow the dough to rise for 1 hour in a warm spot.
Meanwhile, make the filling: combine all ingredients in a bowl, except the mozzarella. Set aside.
Preheat oven to 350°F. Roll out the dough on a lightly floured surface to form a rectangle.
Spread the filling over the dough and make sure to leave an inch around the edges. Sprinkle mozzarella cheese over the top.
Roll the dough into a log lengthwise. Slice the roll in half lengthwise leaving one end (about 1 inch) intact. Twist the two sides into a braid, while trying to keep the cut sides facing up.
Grease a loaf pan and place the braided dough inside. Cover and allow to rise again for about 45 minutes to 1 hour. Uncover, brush with olive oil, and bake for about 30-35 minutes.