Preheat the oven: preheat the oven to 180°C / 350-375°F / Gas Mark 4-5.
Onion and pickles: peel the onion then use a knife and cutting board to quarter it. Place the onion quarters and pickle slices into the food processor and blitz for 2-3 seconds to combine. Remove the slide and use a spatula to scrape down the insides of the bowl then put the lid back on and blitz for a further 2-3 seconds.
Filling: add the beef mince, salt, pepper, panko breadcrumbs, ketchup, mustard and egg to a medium sized mixing bowl. Use clean hands to thoroughly combine.
Egg: crack the egg into a small bowl and use a mini fork to whisk, then set aside.
Pastry: working one sheet at a time place a thawed sheet of puff pastry onto a clean, dry cutting board. Spoon a long shaped amount of the beef mixture along the edge of one side of the square. Next roll the pastry so that it covers the filling and use a basting brush to brush egg wash on the base of the pastry. Push gently down to seal the sausage rolls (slight overlap at base) then cut each long roll into 6 smaller portions. Note 4
Baking tray: spread the individual sausage rolls out across 2 silicon mat lined baking trays. Use a basting brush to coat the top of each sausage roll with the egg wash.
Oven bake: place the 2 baking trays into the oven and cook the sausage rolls for 30 minutes rotating the top and bottom positions of the tray at the half way point.
To serve: once the cheeseburger sausage rolls are cooked, use oven mitts to remove the baking trays from the oven and place them onto a heatproof surface. let them cool for 5-10 minutes and then gently transfer them to a wire rack. Serve with ketchup.