Preheat your oven to 350°F (175°C).

Roll out the pie dough and fit it into a 9-inch pie dish, crimping the edges for a decorative finish.

In a medium mixing bowl, whisk together the packed brown sugar, all-purpose flour, and salt until well combined and no lumps remain.

Gradually whisk in the heavy cream, pure maple syrup, and vanilla extract until the mixture is smooth.

Pour the filling mixture into the prepared unbaked pie shell.

Scatter the small cubes of unsalted butter evenly over the top of the filling.

Bake in the preheated oven for 45 to 50 minutes, or until the filling is bubbling and the crust is golden brown. The center might still be slightly jiggly but will set as it cools.

Remove the pie from the oven and place it on a wire rack to cool completely before slicing. This allows the filling to firm up properly.

Serve at room temperature or chilled, optionally topped with a dollop of whipped cream.