Add olive oil and butter to a large skillet over medium-low heat. Add onions to the pan and gently cook for 20 minutes. Do not let them brown. Keep them over a low heat if they are cooking too fast and stir occasionally. Add garlic and cook for 1 minute. Add salt, pepper, sugar and chopped thyme and cook for 2 minutes. Add white wine and cook until the liquid evaporates. The onions should be browned and sweet.
Preheat oven to 400° F. Open thawed puff pastry onto a floured surface. Cut pastry into 2-3 inch circles or squares. Use scraps for another use. Put the cut pastry on two parchment covered baking sheets in one layer. Score a 1/4 inch border inside the edges of the pastry with a sharp knife, careful not to cut through pastry, and prick the center with a fork.
Sprinkle Parmesan cheese inside the scored lines and add the caramelized onions. Then add a crumble of Joan of Arc Garlic and Herb Goat Cheese and put 3 small slices of tomatoes on top. Finish with a sprig of thyme. Bake, uncovered, for 20 -25 minutes until the pastry has puffed up and turned golden. Serve immediately.