With the rack in the bottom position, preheat the oven to 190°C (375°F).
In a bowl, combine the apples with the sugar and Armagnac. Set aside.
On a clean surface, stack 6 sheets of phyllo, brushing each with butter before adding the next.
Line a 27-cm (10 1/2-inch) tart pan with a removable bottom and 2.5-cm (1-inch) rim with the buttered sheets of dough. Trim off the excess dough, leaving enough to overhang the tart pan by 1 cm (1/2 inch) all around. Set aside the trimmings. Pile the apple mixture on the dough and fold the edges of the dough toward the middle. Set aside.
On a clean surface, brush the remaining sheets of phyllo with butter. Slice each sheet into 3 strips, each about 44 cm (17.5 inches) long. Arrange the dough strips on top of the apples, crumpling them to enhance the impression of height and depth.
Bake until the top is golden, 35 to 40 minutes.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.