In a large bowl, combine the brown onion, garlic, sausage mince, bacon, bread crumbs, tomato paste, vegemite and two eggs.
Prepare the barbecue for indirect cooking over medium heat (180°C to 230°C). If using a Weber Q barbecue, set up your barbecue with a convection tray and a trivet.
Cut a sheet of pastry in half. Shape the mixture into sausages and place in the middle of each half of pastry. Using a pastry brush, brush the edges with egg. Roll up the pastry, to enclose the mixture. Cut each roll into 6 equal portions.
Place the sausage rolls onto lined baking trays. Using a pastry or basting brush, brush the lightly beaten egg on the sausage rolls and finish with a sprinkle of sesame seeds. Repeat with remaining pastry and mince mixture.
Cook the sausage rolls over indirect medium heat for 30 to 40 minutes, with the lid closed, or until the pastry is deep golden.
Serve the sausage rolls with tomato sauce.