Preheat the oven to 200°C (180°C fan/gas mark 6).
Line a large baking sheet with baking paper to prevent the sausage rolls from sticking.
Remove the sausage meat from the skins and place it in a mixing bowl. Add the cheddar cheese and thyme to the sausage meat. Season with salt and pepper to taste, then mash everything together with a fork until combined.
On a floured work surface, unroll the puff pastry sheet and gently roll it out so that it measures 25x48cm (10x19in). This ensures the pastry is thin and crisp once baked.
Divide the rolled pastry into 6 rectangles, each measuring 8x25cm (3x10in). This will ensure even-sized sausage rolls.
Divide the sausage filling into 6 portions and shape each into a long sausage. Place each portion lengthways on one side of each pastry rectangle, leaving a 1cm (½in) border along the edge.
Brush the long edges of the pastry with beaten egg, then fold the pastry over the sausage filling to encase it. Press the edges together to seal, trimming the edges if necessary. Crimp the edges with the back of a fork for a decorative finish.
Chill the rolls (optional): Place the assembled sausage rolls in the fridge for around 10 minutes. This step helps the pastry firm up, resulting in flakier rolls.
Freeze the sausage rolls (optional): Just remember to thaw them completely before baking.
Using a sharp knife, slice each roll diagonally into 5-6 smaller pieces.
Place the sausage rolls on the prepared baking sheet and brush the tops with the remaining beaten egg for a golden finish.
Bake: Bake the sausage rolls in the preheated oven for 25-30 minutes, or until they are golden brown and the pastry is crisp.
Serve and enjoy! Serve the sausage rolls warm or cold as desired.