Preheat oven to 400 degrees F.
Prepare the pie crust and arrange in a DEEP pie plate, crimping edges. Set aside.
Peel and core the apples. Slice them very thin (think 1/8 inch or so--I used a mandolin but a sharp knife works too).
Put them in a bowl and squeeze lemon juice on them after every apple you slice, tossing to coat. This is to add flavor and also to keep the apples from browning.
In a large skillet, heat 4 tablespoons butter over medium heat. Add 1/2 cup sugar and 1 tablespoon pumpkin pie spice.
Add the apples. If you used a lot of lemon juice, don't add all of it. Add 1 teaspoon maximum.
Cook over medium heat for about 3 minutes. Turn the heat up to high and cook for another 2-3 minutes, until the liquid is bubbling and has reduced somewhat. (See photo above).
Pour the apples into the unbaked crust and set aside.
Make the custard. In a medium bowl, whisk together sour cream, egg yolks, and vanilla.
Add the sugar and whisk well.
Gradually add the flour while whisking. Whisk out any lumps.
Pour the custard over the apples, but be careful not to overfill! See photo above. How much you need depends on the size of your pie pan. I used all but about 1/3 cup of the custard.
Place the pie pan on a baking sheet in case it spills over the edge.
Bake at 400 degrees F for 20 minutes. The custard should be starting to set and be golden on top when you take it out of the oven. Decrease the oven temperature to 375 degrees F.
Meanwhile, make the streusel. In a medium bowl, whisk together 1/2 cup flour, 1 tablespoon pumpkin pie spice, and 1/4 cup sugar. Use a fork or pastry cutter to cut in 4 tablespoons cold butter. Cut until you have pea-sized chunks of butter. Keep refrigerated until you are ready to add it to the pie.
Once the pie has baked 20 minutes, remove the pie from the oven and add the streusel topping.
( Don't forget to LOWER the oven temperature to 375.)
Use a pie crust cover*** to cover the crust so it doesn't burn.
Bake an additional 20 to 25 minutes at 375, or until a toothpick comes out clean.
Let sit at room temperature for at least an hour or 2 before cutting into it. I can never wait this long so I always put it in the freezer for 45 minutes or so. Serve with ice cream and caramel sauce! (Recipe below)