Preheat oven to 400˚F. Heat oil over medium and add sausage. Cook until browned. Remove from heat and add Worcestershire sauce, Dijon mustard, Tabasco sauce, thyme, salt, and pepper.
Carefully unroll puff pastry. Cut each sheet in 2 lengthwise. Brush some egg along the edges of each piece. Place some filling into each rectangle of dough. Fold over one long side and then crimp that side with edges of fork.
Cut each sausage roll log into 4 pieces. Clean brush and use it to apply some milk to each sausage roll. Bake for 15-20 minutes or until tops of rolls are golden brown.
