Preheat oven to 350 degrees F.
Lightly dust a work surface with the flour.
Roll the pie crust out on the prepared work surface so that it will fit in a 9-inch pie plate.
Transfer the pie crust to a 9-inch pie plate, then trim and flute the edges.
Line the pie crust with a double thickness of foil.
Fill the pie plate with pie weights or dried beans on top of the foil.
Bake the pie crust on the lower rack of the oven until the edges of the crust are golden-brown, about 15-20 minutes.
Remove the pie weights and the foil and bake the crust again until the bottom is golden-brown, about 3-6 minutes.
Transfer the pie crust to a wire rack to cool.
In a small saucepan, add the cornstarch and the water and whisk to combine until smooth.
Add the maple syrup and the heavy cream to the slurry mixture and stir to combine.
Place the maple mixture over medium-high heat and cook, while stirring, until it is thickened and bubbly, about 2-3 minutes.
Reduce the heat to medium and cook, while stirring constantly, for 2 minutes.
Transfer the maple mixture from the heat.
In a bowl, add the egg yolks.
Slowly add a small amount of the maple mixture to the egg yolks, while whisking them constantly, until they are tempered so that they do not scramble.
Add the egg yolk mixture to the maple mixture in the saucepan and cook, while stirring constantly, until it comes to a gentle boil.
Cook the maple mixture, while stirring, until thickened, about 2 minutes.
Transfer the maple mixture from the heat.
Add the butter to the maple mixture and gently stir to combine.
Pour the maple mixture into the pie crust.
In a large bowl, add the egg whites, the vanilla, and the cream of tartar and use an electric handheld mixer on medium speed to beat until soft peaks form.
Gradually add the the sugar to the egg white mixture, 1 tablespoon at a time and while beating the egg white mixture on high speed, until all of the sugar is dissolved and stiff, glossy peaks form.
Spread the egg whie mixture evenly over the maple mixture, making sure to spread it all the way to the edges.
Bake until the meringue is golden-brown on top, about 12-15 minutes.
Transfer the pie to a wire rack to cool for 1 hour.
Refrigerate the pie for at least 3 hours.
Serve.