To prepare crust, sift the flour and salt in a large bowl. Set aside.
Cream butter and powdered sugar in a bowl of a standing mixer until light and fluffy. Beat in vanilla.
Reduce the speed to low and beat in the flour mixture until just incorporated.
Gather dough and form a dish. Cover with plastic wrap and refrigerate for about 30 minutes to chill.
To prepare apple filling, put apples, butter, sugar, maple syrup and cinnamon in a skillet. Cook over medium heat for about 20 minutes, stirring occasionally, until the apples are very soft and almost fall apart into a puree. Remove from heat and allow to cool to room temperature.
Preheat oven to 350F. Grease a tart pan with a removable bottom.
On a lightly floured surface, roll out the dough to 1/4 inch thickness. Line the prepared pan with the rolled dough. Leave a tiny overhand of dough. Use a small kitchen knife to trim the excess and to score the tops of the tart.
Roll the remaining dough out and cut into 1/2 inch width strips. Lay 3 or 4 strips over the filling, evenly spaced, and then weave with the remaining strips diagonally. Adhere the ends to the edge of the shell.
Bake the tart for 40 to 45 minutes, until the crust is slightly brown on the edges.