I make these often - sometimes the sausage shoots rather rudely out of its skin, sometimes it doesn't. To guarantee your sausage does not escape its roll during cooking, the sausage "skin" can be slipped off before encasing it in pastry.
Preheat the oven to 400 degrees F (200 degrees C).
Roll the pastry out on a floured counter to a rectangle of about 19 x 12 1/2in (48 by 32cm) and bash the pastry with the rolling pin a bit. Puff pastry is made of fine layers and normally you have to be very delicate with it. For sausage rolls the pastry needs to be slightly puffed but not too much, so bashing it with a rolling pin reduces the amount it puffs up.
Cut the large rectangle in half lengthwise, then cut both smaller rectangles into eight equal sections. You now have 16 rectangles in total. Brush one end of each rectangle with a little of the beaten egg and lay a piece of sausage at the other end, then season the sausage with salt and pepper and sprinkle with thyme leaves. Roll the sausage up in the pastry to enclose and repeat with all the sausages. For a flavor variation add sage, parsley, or chopped rosemary. Put the sausage rolls in the refrigerator for 20 minutes for the pastry to harden.
Once the pastry is hard, remove them from the refrigerator and score the tops with a sharp knife for decoration or prick with a fork. Brush well all over with the rest of the beaten egg and bake in the oven for 25 to 30 minutes, or until the pastry has turned a golden brown and looks crisp. Remove from the oven and let cool slightly before serving.