Photograph: Jonathan Gregson
Preheat the oven to 200°C, fan 180°C, gas 6. Bake the sweet potatoes in their skins for 35-45 minutes, until they soften up but are still slightly undercooked in the centre (check by inserting a small knife). Leave until cool enough to handle, then peel and cut into 3mm-thick slices.
Meanwhile, roll out the puff pastry to about 2mm thick on a lightly floured work surface. Cut out six 7 x 14cm rectangles and prick them all over with a fork. Using a small knife held horizontally, gently tap the pastry edges – this will help it to rise. Line a baking sheet with baking parchment, place the pastry rectangles on it, spaced well apart, and chill in the fridge for at least 30 minutes.
Remove the pastry from the fridge and brush lightly with the beaten egg. Spread a layer of soured cream on the pastries, leaving a 5mm border all round. Arrange the potato slices on the pastries, slightly overlapping, keeping the border clear. Season with salt and freshly ground black pepper, crumble over the goats' cheese and sprinkle with the pumpkin seeds and chilli. Bake for 20-25 minutes on the top shelf, or until the pastry is cooked through; it should be golden brown underneath.
Meanwhile, stir together the olive oil, garlic, parsley and a pinch of salt. As soon as the pastries come out of the oven, brush them with this mixture. Serve warm or at room temperature.
Get ahead: the galettes can be made the day before and reheated. They can also be frozen (brush with the oil mixture after reheating).