Preheat your oven to 350℉. Take your pre-made pie crust from the refrigerator and let it sit at room temperature for a few minutes to soften slightly.
Roll out the pie crust and carefully transfer it to a greased 9-inch pie dish. Trim the excess dough around the edges and crimp the edges with your finger or a fork.
Combine the brown sugar, all-purpose flour, and salt in a mixing bowl. Mix well.
In a separate mixing bowl, whisk together the heavy cream, melted butter, eggs and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, whisking constantly until the filling is smooth and well blended.
Pour the filling into a prepared pie crust, smoothing the top.
Bake for 50 to 60 minutes, or until the filling is set and the crust is golden brown. The center may be still slightly jiggly, but it will firm up as it cools.
Remove the pie from the oven and let it cool completely on a wire rack.
Once cooled, refrigerate the pie for at least 2 hours or overnight to allow it to fully set and develop its flavors.
Serve chilled. You can enjoy it as is or add a dollop of whipped cream or a sprinkle of powdered sugar on top, if desired.