Before mixing the dough, be sure to feed your potato flake sourdough starter. Allow it to feed for 8–24 hours so it’s bubbly and active before using. This step is key for good rise and flavor.
In the bowl of a stand mixer, add all dough ingredients except the butter. Using the dough hook, mix on medium speed until the dough begins to pull away from the sides of the bowl.
Cover the bowl with plastic wrap or beeswax wrap and let the dough rest for 10 minutes. This allows the flour to fully hydrate and makes the dough easier to work with.
After resting, remove the cover and knead in the softened butter by hand. This takes a little effort, but it’s much easier than trying to mix it in with the stand mixer, although that can be done as well. Knead until the butter is fully absorbed and the dough feels smooth.
Cover the bowl again and leave it at room temperature to rise until doubled in size — usually 8 to 10 hours.
Once risen, transfer the dough to the refrigerator for about 2 hours. This step isn’t required, but it makes the dough less sticky and much easier to roll and shape.
While the dough chills, prepare the filling.
In a medium saucepan, melt 1 tablespoon butter over medium heat. Add the diced apples and cook, stirring occasionally, until they begin to soften (about 5 minutes).
Reduce the heat to low and stir in the brown sugar and cinnamon. Continue to simmer for about 3 minutes, until the apples are soft and lightly caramelized. Remove from heat and set aside to cool completely.
Preheat your oven to 400°F.
Roll the chilled dough into a rectangle on a lightly floured surface. Using a pizza cutter or sharp knife, cut the dough into 8 equal squares.
Spoon the cooled apple mixture onto half of each square, leaving at least a ½-inch border around the edges.
Fold the dough over the filling to form triangles. Crimp the edges tightly by pinching with your fingers or pressing with a fork to seal.
Transfer the turnovers to a parchment-lined baking sheet, spacing them about 1 inch apart.
If you’d like deep golden brown tops, whisk together 1 egg and 1 tablespoon water and lightly brush over the turnovers.
Bake for 20–23 minutes, or until puffed and beautifully golden.
While the turnovers are still warm, stir together the powdered sugar and heavy whipping cream (adding just enough liquid to reach your desired consistency).
Drizzle or pipe the glaze over the warm turnovers and let it set slightly before serving.