Preheat oven to 350 degrees. Line a baking pan with parchment paper and set aside.
Heat the olive oil in a large skillet and saute the onion slices over low heat until softened. Add the brown sugar and cook 5 minutes more. Next add the wine and some salt and black pepper to taste, and continue simmering the onions on low stirring regularly for about 5 minutes more, until the onions are sticky and caramelized.
Roll out the puff pastry sheet on a lightly floured surface and cut the sheet into 16 equal squares. Use a knife to score small squares inside each piece, without cutting through the pastry to create a ¼ inch border. Separate the pieces and transfer squares onto a parchment lined baking tray and cook for 10 minutes.
Remove the pastry from the oven and use the back of a spoon to push down the centre of the pastry. Then fill each one with caramelised onion and about 1 teaspoon of goats cheese on top. Return them to the oven for another 10 minutes, until the pastry is golden brown. Serve hot or room temperature.