Cut Broccolini® into four crossways. Place sweet potato onto a microwave safe plate in a single layer and cover with damp paper towel. Microwave on High/100% for 4-5 minutes until almost tender.
Heat oil in a large frying pan over medium-high heat. Add mince and cook stirring with a wooden spoon to break up mince, for 5 minutes or until browned. Add curry paste and cook, stirring occasionally for 3 minutes. Add coconut milk and sweet potato, bring to simmer. Simmer for 2 minutes, then stir in Broccolini®. Refrigerate to cool.
Use the pie maker pastry cutter to cut 16 large rounds from shortcrust sheets and 16 small rounds from puff pastry sheets. Lightly grease the pie maker and press 4 shortcrust rounds into the pie holes. Fill with about 1/2 cup massaman mixture and top with the 4 small rounds. Cut a cross in the centre of each and brush the tops with egg. Turn on the pie maker, close and cook for 8-10 minutes or until pies are golden.
Repeat with the remaining pastry and filling. Serve with yoghurt and chilli sauce.