Preheat oven to 400ºF.
Dust a countertop lightly with flour and lay one sheet of puff pastry down. Roll the dough out lightly until it measures approximately 10x12". Cut the sheet in half lengthwise, then cut each piece into thirds widthwise, leaving you with 6 portions. Repeat with the other sheet of puff pastry.
Cut the tail and root off from each onion and peel them, leaving the onion intact. Make two deep cuts into the top of the onion to form an X, , taking care to cut only three-quarters of the way through the onion. Arrange the onions cut side up on a plate and sprinkle the Worcestershire, grill seasoning, brown sugar, thyme and a little cheese evenly over each one. Transfer each onion to a square of puff dough.