Start by getting your puff pastry out of the freezer about 30 minutes before you need it – you want it thawed but still cool to touch.
While the pastry’s thawing, finely dice your onion and grate the carrot. You want the vegetables really fine so they cook through and blend seamlessly into the filling.
In a large bowl, mix together your sausage meat, diced onion, grated carrot, chopped herbs, and breadcrumbs. Season well with salt and pepper with about 1 teaspoon of salt and 1/2 teaspoon of pepper.
Preheat your oven to 200°C (400°F) and line two baking sheets with parchment paper. Beat your egg in a small bowl with a fork and set aside.
Once your pastry is thawed but still cool, lay it out on a lightly floured surface. Cut each sheet in half lengthwise so you have four long rectangles. Working with one rectangle at a time, spoon the sausage mixture down the center, forming a long sausage shape about 3cm (1 inch) in diameter, leaving about 2cm of pastry clear on either side.
Brush one long edge of the pastry with beaten egg, then carefully lift the other edge and roll it over the filling, sealing it where you brushed the egg. The seal should be on the bottom. The pastry should overlap slightly – if it doesn’t, your filling line might be too thick.
Cut each long roll into pieces about 5cm (2 inches) long. Make three small diagonal cuts on top of each roll – this lets steam escape and looks pretty. Brush the tops with beaten egg and sprinkle with sesame seeds if using.
Place the rolls on your prepared baking sheets, leaving some space between each one as they’ll puff up. Bake for 20-25 minutes – you’re looking for a rich golden brown color and the pastry should be visibly layered and crisp. If you lift one up, the bottom should be golden too, not pale.
Let them cool on the tray for about 5 minutes before moving.