Cook pasta until mushy. Let cool; drain. Add salt and purée in a food processor or mix by hand until it forms a sticky dough.
Divide dough in half; flatten between sheets of greased parchment paper and chill. Roll dough until ⅙″ thick.
Cut out circles with a round cutter. Place 1 slice mozzarella and 2 tbsp. filling over each circle; fold in half and pinch edges.