Line a baking sheet with parchement paper, and unfold the puff pastry in order to place it in the middle of the baking sheet. Prick the sheet, cover with plastic and refrigerate.
Preheat oven to 425 degrees F.
In a large skillet, heat olive oil over medium high heat. Add leek and cook until softened, about 3 minutes. Add Brussel sprouts, salt and pepper, and cook, stirring occasionally for about 5-7 minutes (this is to make sure the Brussel Sprouts brown).
Add balsamic vineger and continue to cook until the liquid is absorbed, and put into a bowl to mix with the thyme. Let cool.
Take the puff pastry out of the fridge and spread the vegetable mixture, leaving a 1 inch border all around. Brush edges with egg and sprinkle with cheese. Bake until the pastry is golden and the cheese is bubbling, about 20 minutes.
Cool slightly and serve warm, or serve at room temperature if you like.