Set your oven to preheat at 180°C (or 160°C for fan-assisted ovens). Begin by placing the flour into a large mixing bowl and adding the diced, chilled butter. Using your fingertips, rub the butter into the flour until the mixture resembles coarse breadcrumbs. Pour in the cold water and mix with a round-bladed knife until the dough just comes together. Form into a ball, wrap in clingfilm, and refrigerate for at least 10 minutes to firm up.
Meanwhile, heat a large frying pan over medium heat. Drizzle in the olive oil, then add the mushrooms. Sauté for about 5 minutes, stirring occasionally, until they are softened and golden around the edges. Remove from heat and let them cool slightly while you prepare the rest.
Lightly flour your work surface and roll out the chilled pastry to a thickness of approximately 5mm. Carefully line a 25cm loose-bottomed, fluted tart tin (around 3cm deep) with the pastry. Prick the base with a fork to prevent bubbling. Place a sheet of parchment over the pastry and fill it with baking beans. Blind bake in the preheated oven for 10 minutes. Then, remove the paper and beans, and return the tart shell to the oven for another 5 minutes until lightly golden and cooked through.
While the tart shell is baking, whisk together the eggs and double cream in a bowl until smooth. Stir in the grated Vasterbottensost, then season with a pinch of sea salt and freshly cracked pepper.
Take the tart shell out of the oven and scatter the cooked mushrooms evenly across the base. Pour over the creamy egg and cheese mixture, making sure it spreads evenly. Return the filled tart to the oven and bake for about 20 minutes, or until the custard is just set and lightly golden on top.
Once out of the oven, let the tart cool slightly. Trim away any excess pastry for a clean edge, then slice generously and serve warm or at room temperature.