1. In a food processor, pulse the flour and salt together. Add the chilled butter cubes and pulse until the mixture resembles coarse crumbs. Gradually add the ice water and pulse just until the dough begins to hold together. Form the dough into a disc, wrap in plastic, and refrigerate for at least 1 hour.

2. Preheat the oven to 400°F (200°C). On a lightly floured surface, roll the dough out into a 12-inch circle, about 1/4-inch thick. Transfer the dough to a baking sheet lined with parchment paper.

3. Arrange the apple slices in concentric circles on the dough, leaving a 2-inch border. Fold the border over the apples, pleating it as you go.

4. In a small saucepan, combine the sugar and miso paste. Cook over medium heat, stirring constantly, until the mixture turns golden and caramelized, about 5-7 minutes. Slowly pour in the heavy cream and whisk until smooth. Drizzle the miso caramel over the apples.

5. Brush the exposed dough with the egg wash.

6. Bake for 35-40 minutes, or until the crust is golden brown and the apples are tender. Allow to cool for at least 30 minutes before serving.