Preheat your oven to 200°C (400°F) or 180°C fan and line a baking tray with parchment paper. In a mixing bowl, combine the rolled oats, chopped hazelnuts, flour, brown sugar, and salt. Add the cold butter and rub it into the dry ingredients using your fingertips until the mixture resembles coarse crumbs. Place the crumble in the refrigerator while you prepare the filling.
Lay the puff pastry sheet onto the prepared baking tray. If desired, lightly score or fold a 1–2 cm border around the edges to help create a raised crust. Brush the border generously with beaten egg to encourage a beautiful golden finish during baking.
In a large bowl, gently toss the sliced peaches with the brown sugar, flour, ground cardamom, and fresh lemon juice until every slice is evenly coated. The flour will help thicken the juices while the peaches bake.
First, sprinkle a thin layer of the hazelnut crumble over the centre of the puff pastry, leaving the egg-washed border uncovered. Next, arrange the peach slices in a checkerboard pattern by placing one group of slices parallel to each other, then alternating the next group at a right angle. Continue this pattern until the tart is completely covered. Finally, scatter the remaining crumble evenly over the peaches.
Transfer the tart to the preheated oven and bake for 35–45 minutes, or until the puff pastry is deeply golden, the crumble is crisp, and the peaches are tender and bubbling around the edges.
Allow the Peach & Hazelnut Crumble Pie to cool for 10–15 minutes before slicing. Serve warm on its own or with vanilla ice cream, whipped cream, or freshly whipped cream for an extra indulgent dessert.