I took the best of several recipes to make it my own, and so my version is reflected below.
FOR THE CRUST
Prepared pie crust -- I always use David Letterman's mother's recipe
FOR THE FILLING
1 butternut squash, about 1 1/2 pounds (will yield 6 cups of cubed squash after peeling and de-seeding)
3 large eggs plus 2 large egg yolks (see ideas for the extra egg whites here.)
1 cup heavy cream
1/2 cup packed brown sugar (I used light, but don't think it matters)
2 T applesauce (original recipe called for 2 T brandy, but I don't have that sitting around...)
2 tsp ground cinnamon
1/2 teaspoon ground nutmeg
Salt and pepper
Lightly sweetened freshly whipped cream, for serving
NOTE: Most of the pumpkin pie recipes I looked at had the traditional combination of cinnamon, allspice, nutmeg, and cloves. I just don't happen to enjoy the flavors of allspice and cloves, but feel free to remain traditional in your baking of this pie!
Preheat oven to 375 degrees. Make the crust: Roll out the pie crust to a 1/8-inch thickness on a lightly floured surface. Fit dough into a 9-inch pie plate, and trim crust to a 1-inch overhang. Fold edges under, and crimp as desired. Freeze until firm, about 30 minutes. Bake until edges of crust begin to turn golden, about 20 minutes. Let cool on a wire rack.
For the filling, peel and de-seed the butternut squash, and then cut into small cubes. Cook the squash by your favorite method; I use my electric steamer, but you can boil, roast, microwave, etc.
Put cooked squash in your food processor or mixer, and process until smooth and light.
Reduce oven temperature to 325 degrees. Whisk squash puree, eggs, egg yolks, heavy cream, sugar, applesauce, cinnamon, nutmeg, 3/4 teaspoon salt, and a pinch of pepper in a bowl.
Pour filling into pie shell, and bake until just set but still slightly wobbly in the center, about 1 hour (filling will continue to set as it cools). Let cool on a wire rack. Serve slightly with whipped cream.