Prepare the Ingredients: Preheat your oven temperature to 400°F (200°C). Start by heating the olive oil a frying pan and sautéeing pancetta for about 4-5 minutes. When crispy, set aside on a paper towel to drain using a slotted spoon.
Cook the Leeks: In the same pan, cook the sliced leeks seasoned with a pinch of salt and pepper until they are soft on medium heat, about 7-10 minutes. Add chopped tarragon at the last minute, then remove from heat.
Prep the Pastry: On a lightly floured work surface, roll out the puff pastry into a rectangle about ¼-inch thick with a rolling pin. Transfer to a baking sheet lined with parchment paper. With a knife, trace a ½ inch border, and gently pierce the base of the tart with a fork.
Assemble the Tart: Sprinkle the grated Gruyere cheese onto the puff pastry. Spread the leek mixture over the cheese, and then layer the crispy pancetta on top. Brush the border with egg wash.
Bake: Bake in the preheated oven for about 20-25 minutes, or until the edges of the pastry is golden brown and puffed.
Serve: Remove from oven, top with additional fresh tarragon, and serve immediately.