Preheat oven to 220°C/425°F. In a small bowl, combine the ricotta and the egg. Mix until the egg is well incorporated. Season with salt and pepper. Set aside.
Working one sheet at a time and keeping the remainder of the phyllo pastry covered under a damp tea towel, lay a sheet of pastry on a clean work surface and brush liberally with butter. Gently top with another sheet of pastry, brush with butter and repeat until all 6 sheets have been used. Do not brush butter over the top sheet of pastry.
Using a 10cm/4in wide circular cutter, cut 10 circles out of the prepared dough.
Working one circle at a time, spoon a tablespoon of ricotta filling into the centre of the circle. Fold the circle in half over the filling and pinch the ends together. Flatten the bottom on the work surface and transfer to a parchment-lined baking sheet. Repeat with the remaining dough circles.
Brush the formed pastizzi with the remaining melted butter and then transfer to the oven. Bake for about 10 minutes, or until the pastry is a deep golden brown and the filling is puffed. Allow to cool for at least 5 minutes before eating.