Italian star bread

Ingredients
Dough
240 ml full cream milk room temperature
1 teaspoon dried yeast
2 teaspoons castor sugar
500 g flour
60 g unsalted butter softened
1 egg
1 ½ teaspoons salt
Pesto Filling
40 g parmesan grated
1 small bunch basil
40 g salted and roasted macadamia or cashew nuts
1 clove garlic
60-70 ml extra virgin olive oil
Mozzarella filling
125 g tomato paste
¾ teaspoon salt
¼ teaspoon pepper
1 tablespoon Italian herbs dried
10 ml extra virgin olive oil
160 g mozzarella cheese finely grated
Other
1 egg for egg wash