Step 1: Preheat your oven to 375°F (190°C). Roll out your pie dough and fit it into a 9-inch deep-dish pie plate. Trim and crimp the edges, then chill in the refrigerator.
Step 2: In a large mixing bowl, combine the sliced apples, lemon juice, granulated sugar, 1/4 cup brown sugar, cinnamon, nutmeg, and cornstarch. Toss well to coat every slice.
Step 3: Prepare the streusel by mixing the flour, oats, 1/2 cup brown sugar, and cinnamon in a medium bowl. Use a pastry cutter or your hands to work in the cold butter until the mixture is crumbly with various sized lumps.
Step 4: Arrange the apple mixture in the chilled pie crust, mounding them slightly in the center. Pour any leftover juices from the bowl over the apples.
Step 5: Generously cover the apples with the spiced brown sugar streusel, pressing lightly to ensure it stays in place.
Step 6: Place the pie on a parchment-lined baking sheet and bake for 55-65 minutes, or until the topping is golden brown and the apple juices are bubbling thickly around the edges.
Step 7: Allow the pie to cool on a wire rack for at least 2 hours before slicing. This is crucial for the filling to set properly.