Grind coriander, chilli, ginger, and lemon juice into a smooth paste.
Mix the paste with chaat masala, sesame seeds, black salt, salt, and black pepper.
Stir in the grated boiled potato until well combined and lump-free.
Take one sheet of puff pastry. Lightly dust the top with all-purpose flour.
Cut a circular shape from a puff pastry sheet.
Flip the circle. On one semi-circle half, lightly dust flour and make several diagonal cuts. Keep the edges clear.
Spread potato mixture over the un-cut half, leaving a border.
Fold the scored side over the filling to form a semi-circle. Press and seal the edges firmly.
Bring one corner of the semi-circle to the center, then overlap with the other corner to form a triangular/cone shape (the "tree"). Seal the final corner.
Transfer to a lined tray. Brush with milk and sprinkle sesame seeds.
Bake in a preheated oven at 180 degree Celsius for 30–35 minutes, until golden and puffed.
Use a star-shaped cookie cutter to cut star shapes from the cheese slices.
Immediately after baking, place a cheese star on top of each samosa tree. Serve warm!