Brush a baking dish with clarified butter. Lay down two sheets of phyllo dough, brush with butter, and repeat, brushing butter between every two sheets, until you use half the package.

Spread the mixed cheeses in the center. Continue layering two sheets of phyllo at a time, brushing butter between each pair, until you finish the remaining half of the dough. Cut the assembled goulash into pieces and cover for 5 minutes.

Prepare the soaking mixture: In a bowl, combine 2 cups milk, 2 eggs, salt, black pepper, and baking powder. Mix well, then pour over the cut goulash so it absorbs the mixture. Cover and let sit for another 10 minutes. Bake in a preheated oven. After 15 minutes, remove from the oven and sprinkle mozzarella cheese on top. Return to the oven until the cheese melts and the top is golden brown.