Step 1: In a large mixing bowl, combine the all-purpose flour, baking powder, and a pinch of salt. Whisk these dry ingredients together until well incorporated.
Step 2: Add the vegetable oil and yogurt. Use a fork or your hands to mix until the mixture resembles coarse crumbs. Then, mix in the cold water and apple vinegar, just until the dough holds together. Avoid over-mixing to keep it tender.
Step 3: Form the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes while you prepare the filling.
Step 4: While the dough chills, wash and slice both the apples and plums. Remove the pits from the plums and slice them thinly to match the apple slices.
Step 5: In a mixing bowl, combine the sliced apples and plums with the ground cinnamon and granulated sugar. Toss gently until the fruit is evenly coated. Set aside to allow the flavors to meld.
Step 6: Preheat your oven to 375°F (190°C). Once the dough has chilled, remove it from the refrigerator. On a lightly floured surface, roll out the dough into a roughly 12-inch circle.
Step 7: Transfer the rolled-out dough to a baking sheet lined with parchment paper for easy cleanup.
Step 8: Arrange the fruit mixture in the center of the dough, leaving about a 2-inch border around the edges. Gently fold the edges of the dough over the fruit, pleating it to create a beautiful border.
Step 9: Using a pastry brush, gently apply the beaten egg over the folded edges of the dough.
Step 10: Bake the galette in your preheated oven for about 30-35 minutes, or until the crust is golden brown and the fruit is bubbling.
Step 11: Allow the galette to cool for at least 10 minutes before slicing. Enjoy warm or at room temperature.
Notes
Chill the dough for a flaky crust. Feel free to experiment with other fruits or spices!