To prepare the dough, mix the flour, brown sugar, bicarbonate of soda, salt and lard together with your fingertips. Rub together until the consistency is like fine breadcrumbs.
Mix the vinegar with the beaten egg and add enough cold water to bring the volume up to 225 ml.
Add the wet ingredients to the dry, mixing well with a wooden spoon until the dough comes together.
Turn out onto a floured board and knead for a few minutes until it forms a smooth ball.
Divide the dough into two and shape into flat, round discs. Wrap in cling film and refrigerate until needed.
To prepare the filling, finely chop the leftover roast lamb into 5mm or smaller dice. Add the remaining ingredients and stir well to combine. Refrigerate until needed.
Preheat oven to 220 C/ 200 C fan and line a baking tray with greaseproof paper.
Roll out each disc of pastry to the thickness of a pound coin. Using a sharp knife carefully cut the dough into 3.5 inch squares.
Arrange one tablespoonful of the lamb and mint filling down the centre of each square.
Brush a little beaten egg along one side of square and fold over the two sides so that the egg wash side sticks to the other side to form a sausage roll shape.
Brush the tops with beaten egg and prick with the tines of a fork two times to let steam escape.
Bake for 20-25 minutes until golden. Transfer to a wire rack to cool.
If using the ready made puff pastry, allow to come to room temperature for a half an hour before rolling out into a rectangle shape the thickness of a pound coin.
Using a sharp knife carefully cut into two long rectangles about 4 inches wide and 15 inches long.
Arrange the lamb and mint filling along the centre of each rectangle and brush beaten egg down the pastry on one side. Fold over the pastry to seal.
Using a serrated knife, cut each piece into 9 sausage rolls and arrange on a baking tray.
Brush the tops with beaten egg and sprinkle with sesame seeds.
Bake for 20-25 minutes until golden. Transfer to a wire rack to serve.
Serve the sausage rolls hot or cold with hot tomato pickle, if desired.