Preheat oven to 425°F and line a baking sheet with parchment paper. Drizzle the center of the parchment paper with olive oil. The size should match the dimensions of your piece of puff pastry.
Place the onions, shallot, olives, feta, salami, pimento sauce, and parsley decoratively over the olive oil. Sprinkle with salt, keep in mind that many of the ingredients are already salty, so do this with a light hand. Drizzle the remaining olive oil over the ingredients.
Drape the puff pastry over the ingredients on the parchment. Bake for about 20 minutes or until the puff pastry is caramel brown in color and evenly puffed, the center will puff last.
Carefully flip the tart over onto a serving tray or cutting board. If the onions and other ingredients are not fully cooked, slide the tart back onto the baking sheet, onion side up this time and return to the oven for another 5+ minutes or until the onions are golden brown on the edges.
Add more parsley and a sprinkle of Piment d’Espelette before serving. It can be eaten hot or at room temperature.