Preheat your oven to 375°F (190°C).

Fit the unbaked pie crust into a 9-inch pie dish and crimp the edges decoratively.

In a medium mixing bowl, whisk together the packed brown sugar, flour, and salt until there are no lumps.

Gradually pour in the heavy cream, pure maple syrup, and vanilla extract, whisking constantly until the mixture is completely smooth.

Pour the liquid filling into the prepared pie shell.

Scatter the small cubes of butter evenly over the surface of the filling.

Bake in the preheated oven for 40 to 45 minutes, or until the filling is bubbling and the crust is golden brown. The center should still be slightly jiggly like gelatin.

Remove from the oven and place on a wire rack.

Allow the pie to cool completely (at least 2 hours) before slicing to ensure the filling sets properly.