1. Preheat the oven to 425°F with a rack in the center position.

2. Melt ½ cup of the butter in a large pot over medium heat. Add ¼ cup of the flour and stir until a paste forms, 1 to 2 minutes. Stir in the white sugar, lemon juice, ¼ cup water, ¼ cup of the brown sugar, 1 teaspoon of the cinnamon, and ½ teaspoon of nutmeg. Increase the heat to high and bring to a boil, stirring often. Reduce the heat to low and simmer until the sugars begin to dissolve, 3-5 minutes. Remove the pot from the heat. Add the sliced apples and toss to coat.

3. On a lightly floured surface, roll out the pie dough into a 14-inch round. Carefully transfer the round to a 9-inch, deep dish pie plate. Gently press the dough into the bottom and sides without stretching. Trim the edges if necessary. Gently press the tines of a fork into the edge of the dough to crimp.

4. Cut the remaining stick of butter into 8 pieces and add to the base of a food processor. Add the remaining 1 cup of flour, remaining ¾ cup of brown sugar, remaining 1 teaspoon of cinnamon, remaining ½ teaspoon of nutmeg and the vanilla. Pulse until pea size crumbles form, about 8-10 times.

5. Spoon the apple filling, including the liquid, into the prepared dough, forming a slight mound in the center. Evenly top the apple filling with the streusel.

6. Place the pie plate on a rimmed sheet pan and bake for 15 minutes. Reduce the oven temperature to 350°F and continue baking, until the crust and streusel are golden brown and the filling is bubbling, about 45 minutes more. If the pie crust or streusel begins browning too quickly, tend the pie loosely with foil.

7. Cool on a baking rack for at least 2 hours before serving.

Note: If you don’t have a food processor, use a large bowl and a pastry cutter to cut the remaining stick of butter into the flour, brown sugar, cinnamon, nutmeg and vanilla until pea size crumbles form.