Preheat oven to 350°F and put pie crust in pie pan. Prick crust all over, add parchment paper or foil pressed to the shape of the crust and pie weights (I use dried beans) and bake for 20 minutes.
In a large bowl, whisk eggs until lightly frothy. Whisk in butternut squash puree, cream, brown sugar, vanilla, and spices, mixing until completely smooth.
Set pie pan on a rimmed baking sheet (in case of spillage) and pour filling into crust. Cover edges with a pie shield or strips of foil, if desired. Carefully slide the baking sheet into oven and bake the pie for about 45 minutes, until filling is set but still slightly wobbly.