Place grated vegetables in a clean tea towel or paper towels and squeeze out as much liquid as possible — this helps avoid soggy sausage rolls.
Heat olive oil in a saute pan or sauce pan large enough to hold all of the grated veggies. Add garlic and cook until beginning to soften. Add grated vegetables and cook until fully softened, slightly browning and remaining liquid cooked out. Cool to room temperature and drain any excess liquid.
Add cooled vegetable mixture and remaining ingredients except for 1 egg and the puff pastry, to a large mixing bowl and mix until fully combined.
Make Sausage rolls
Preheat oven to 180 C and line a baking tray/s with parchment paper.
Cut one sheet of thawed puff pastry in half. For each half sheet of puff pastry, shape the filling into a log running along the long edge of the pastry around 3–4 cm thick leaving about 2 cm border at the edge for sealing (enough filling that the pastry wraps around comfortably without stretching tightly or leaving huge empty pastry overlap).
Brush the opposite long edge lightly with beaten egg or water. Roll the pastry over the filling so the seam sits underneath.
Cut to size - use a sharp knife to cut each long roll into 3 large sausage rolls, or 5–6 party-sized pieces
Arrange seam-side down onto baking trays lined with baking paper, leaving a little space between each roll.
Brush the tops generously with beaten egg and sprinkle tops with sesame seeds.
Bake in oven for approximately 30 minutes or until pastry is golden brown and meet is cooked through.
After baking and cooling, the sausage rolls can be frozen for up to 3 months