Preheat your oven to 200°C (about 390°F).
In a large bowl, combine the ground lamb, grated pumpkin, chopped onion, minced garlic, chopped rosemary, chopped thyme, crumbled feta cheese, ground nutmeg, chilli flakes (if using), and salt and pepper. Use your hands to mix together until well combined.
Lay out your puff pastry sheets on a clean surface. Divide the lamb and pumpkin mixture into two, shaping each half into a log along one edge of the pastry sheet.
Roll the pastry sheet tightly around the filling, brushing the far edge of the pastry with the beaten egg to help seal it. Repeat with the second pastry sheet and the remaining filling.
Cut each roll into your desired size (typically 5-6 pieces per roll). Arrange the sausage rolls on a baking tray lined with baking paper. Make sure to leave space between them to allow for expansion during baking.
Brush the pastry with the remaining beaten egg, then sprinkle with black and white sesame seeds if you like.
Bake in the oven for 25-30 minutes or until the pastry is golden brown and the filling is cooked through.
Allow to cool slightly before serving. Enjoy your homemade Lamb and Pumpkin Sausage Rolls!