How to Make It
In a large skillet, heat the olive oil until shimmering. Add the onions, rosemary and a generous pinch of salt and cook over moderate heat, stirring occasionally, until soft and caramelized, 40 to 45 minutes. Stir in the vinegar and garlic and cook until the mixture is fragrant and the vinegar evaporates, about 2 minutes. Stir in the parsley and season with salt. Let cool completely. Discard the rosemary sprig.
Meanwhile, roast the red pepper directly over a gas flame or under the broiler, turning, until charred all over. Transfer the pepper to a bowl, cover tightly with plastic wrap and let cool, about 15 minutes. Peel, stem and seed the pepper, then cut into thin strips.
Preheat the oven to 375°. Line a large rimmed baking sheet with parchment paper. On a lightly floured work surface, roll out the puff pastry to a 12-by-14-inch rectangle. Slide the pastry onto the parchment–lined baking sheet and poke it all over with a fork. Top with another sheet of parchment and a baking sheet and bake for 20 to 25 minutes, until the pastry is lightly browned. Remove the top baking sheet and parchment paper and bake the pastry for 15 minutes longer, until slightly puffed and browned. Let cool for 5 minutes.
Spread the cooled onions evenly over the pastry, then top with the roasted pepper strips, anchovies and olives. Cut into squares and serve.