Prepare the Crust: Preheat your oven to 375°F (190°C). Roll out the pie crust and fit it into a 9-inch pie pan. Trim and flute the edges. Line the crust with parchment paper and fill it with pie weights or dried beans. Bake for 15-20 minutes until the edges are lightly golden. Remove the parchment paper and weights, and bake for another 5-7 minutes until the crust is fully baked and golden brown. Let it cool completely.
Make the Filling: In a medium saucepan, combine the maple syrup, light brown sugar, cornstarch, and salt. Gradually whisk in the heavy cream until the mixture is smooth. Cook over medium heat, whisking constantly, until the mixture thickens and comes to a boil. Boil for 1-2 minutes, then remove from heat.
Add Butter and Vanilla: Stir in the butter and vanilla extract until the butter is fully melted and the mixture is smooth.
Fill the Crust: Pour the maple cream filling into the cooled pie crust. Smooth the top with a spatula.
Chill the Pie: Refrigerate the pie for at least 4 hours, or until fully set.
Serve: Slice and serve the pie chilled. Optionally, top with whipped cream or a drizzle of extra maple syrup.