Heat the oven to 170°C/150°C fan/325°F/Gas 3.
Steam or boil the sweet potato until tender. Drain well, mash until smooth and leave to cool.
Weigh the mashed sweet potato and spoon 125g into a mixing bowl – you can freeze any leftover for another time, or stir it into soup or hummus (for humans, obviously).
Mix the peanut butter and egg into the sweet potato. Add the dried cranberries, fresh or dried parsley and the oats and mix again. Add the flour and, using your hands, mix until thoroughly combined.
Roll out the mixture on a lightly floured work surface until about 2–3mm thick. Using the cutter, stamp out as many shapes as you can, re-rolling the trimmings as necessary (you should get about 25 bone shapes). Arrange the dog biscuits on the lined baking sheet.
Bake the biscuits on the middle shelf for about 15 minutes, or until crisp and starting to turn pale brown around the edges. Leave to cool on the baking sheet – they will crisp further as they cool. Store in an airtight box or tin and serve as a treat for good behaviour!