Fit the pie dough into a 9-inch pie plate. Trim and crimp the edge, then refrigerate it while preparing the filling.
Peel, core, and cut the apples into slices about 1/4 inch thick. Toss them with the lemon juice.
Add the apples, granulated sugar, brown sugar, cinnamon, nutmeg, salt, flour, and 2 tablespoons of butter to a large skillet.
Cook over medium heat for 6 to 8 minutes, stirring gently, until the apples begin to soften and release their juice. Remove from the heat and stir in the vanilla.
Transfer the filling to a wide bowl or rimmed pan. Let it cool for about 20 minutes.
To make the topping, whisk the flour, brown sugar, cinnamon, and salt in a medium bowl.
Stir in the melted butter until the dry ingredients are evenly moistened. Let the mixture rest for 5 to 10 minutes.
Place a rimmed metal sheet pan in the oven. Preheat the oven to 400°F.
Spoon the cooled filling into the chilled crust. Mound the apples slightly in the center.
Squeeze and break the streusel into crumbs. Scatter the crumbs evenly over the apples without pressing them down.
Place the pie on the hot sheet pan and bake at 400°F for 20 minutes.
Reduce the oven temperature to 375°F and bake for another 35 to 45 minutes.
Cover the top or crust edge loosely with foil if either begins to brown too quickly.
Remove the pie when the topping is golden, the apples are tender, and the filling bubbles around the edges and near the center.
Cool the pie on a wire rack for at least 3 hours before slicing.