In a large skillet, heat butter over medium heat. Add the onions, fennel, white wine, and a pinch of salt, and sauté for 20-30 minutes, stirring frequently, until vegetables are dark brown and fragrant. Remove from heat and set aside.
While the onions and fennel are cooking, mix the chevre, one beaten egg, fresh rosemary, and a pinch of salt and black pepper in a small mixing bowl. Blend well and set aside.
Carefully remove the puff pastry from its package and lay it on a floured surface (if necessary, roll out the pastry dough into a large rectangle). Cut the dough into 12 equal rectangles. Place the rectangles on a baking tray lined with parchment paper. Fold over ¼ inch of dough around each edge to make a small border to contain the filling. Beat the other egg to make an egg wash. Brush just the folded edges of the puff pastry with egg wash.
Gently spread equal amounts of softened goat cheese mix on each of the rectangles of dough. Divide the caramelized onions and fennel over the top of the goat cheese. Sprinkle each tart with a few pine nuts and a little Parmesan cheese. Place the baking tray in the oven and bake for 25-30 minutes until the pastry is puffy and just starting to brown.