Heat the olive oil over medium heat, in a large frying pan. Add leeks and onion, and sauté for about 5 minutes, stirring occasionally until wilted. Stir in the garlic and continue to sauté for about 1 minute. Add spinach and cook for about 2 minutes, until wilted and softened. Add the olives. Remove the mixture from the heat. Adjust seasoning to taste.

Meanwhile, combine the cheese with 2 eggs in a large bowl. Fold in the vegetables mixture until all ingredients are well combined.

Preheat oven to 375 F/ 190ºC.

Unwrap the puff pastry sheet onto a clean, lightly floured surface and using a rolling pin roll it open a little, so that it is larger than the periphery or circumference of the tart pan you are using. Cover the tart pan with parchment paper. Transfer the dough into the tart pan. Fill the tart with the spinach mixture. Roll the excess puff pastry dough around the circumference or periphery of the pan to form a rim. In a small bowl, whisk the remaining egg and brush the uncovered part of the filling.

Bake for about 45 minutes, until the dough turns golden and sets. Remove the tart from the oven and let it sit for 10 minutes before serving.