Preheat oven to 400F.
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.
In a small bowl, whisk the egg yolks with splash of water or milk. Brush the border of each puff pastry square with an onion on it lightly with the egg wash. Lay another piece of pastry over the top. Try to keep out as much as air possible, you really want to hug the onion.
Press the dough together at the base to seal and cut off the excess to form squares, leaving a half-inch border of dough around the onion. Using a fork, crimp the edges and brush the entire top with egg wash. Sprinkle the remaining cheese over the pockets.
Transfer the pockets to a baking sheet and bake until golden brown, about 40 minutes. Serve warm.