Make the pastry dough: In a food processor, combine the flour, sugar, salt, and butter. Pulse until the mixture resembles wet sand. While pulsing, slowly drizzle in the water and continue to pulse until the dough comes together. Gather the dough into a ball. (Wipe the food processor bowl clean and set aside.) At this stage the dough can be flattened into a disc, wrapped in plastic wrap, and stored in the refrigerator for up to 2 days.

On a lightly floured work surface, use a rolling pin to roll out the dough into an 11-inch circle, ⅛ inch thick. Gently lift the dough into a 9-inch tart pan with removable bottom and press the dough onto the bottom and up the sides (but not into the creases) of the pan.

With a sharp knife, cut excess pastry from the top of the pan. Chill in the refrigerator for 15 minutes.

Make the filling and bake: Preheat the oven to 375°F (190°C).

In the food processor, combine the sweet potatoes, brown sugar, eggs, butter, milk, cinnamon, and nutmeg. Process until smooth. Pour the filling into the chilled pie shell. Bake until the filling is set and a knife inserted into the centre of the pie comes out clean, 60 to 65 minutes. Transfer the pie to a rack to cool completely before piping the maple meringue.

Make the maple meringue and finish: In the bowl of a stand mixer fitted with the whisk attachment, combine the egg whites, maple syrup, maple extract, cream of tartar, and salt. Whip on low speed until the mixture is foamy, then increase to medium-high and continue whipping until stiff peaks form, about 3 minutes.

Spoon the meringue into a piping bag fitted with a plain medium tip. Pipe 3-inch peaks of meringue over the filling. (Alternatively, spoon dollops of meringue over the filling and use a spoon to shape peaks.) Use a kitchen torch to lightly toast the meringue evenly until golden brown. Let the pie cool completely, uncovered, in the refrigerator before slicing.

When ready to serve, release the sides of the pan. This pie is best served the day it is made but can be refrigerated for up to 2 days.