Apple and Armagnac Phyllo Pie (Tourtière Landaise)

In a small saucepan, warm the butter over medium-low heat until completely melted. Remove the pan from the heat and let the butter stand for 10 minutes. Skim off and discard the foam on the surface, then slowly pour the clarified butter into a bowl, discarding any remaining solids. Add the armagnac, rum, and vanilla to the butter and stir to combine.

Heat the oven to 350° and grease an 8-inch pie dish with butter. Using a pastry brush, brush one sheet of phyllo with the clarified butter and armagnac mixture, crumple into a loose ball, and place it in the bottom of the prepared dish. Repeat this process with 8 more phyllo sheets, covering the bottom of the dish. Sprinkle the phyllo with 2 tablespoons granulated sugar, then top with half the apple slices. Brush 9 more sheets of phyllo with the clarified butter and armagnac mixture and crumple and arrange them over the apples. Sprinkle the phyllo with 2 tablespoons granulated sugar, then top with the remaining apple slices. Brush 9 more sheets of phyllo with the clarified butter and armagnac mixture and crumple and arrange them over the apples. Drizzle the pie with any remaining butter-armagnac mixture, then sprinkle the phyllo with the remaining 2 tablespoons granulated sugar. Bake until the phyllo is golden brown and the apples are tender, 45 to 50 minutes.

Transfer the pie to a rack and let cool for 10 minutes. Unmold the pie and serve while hot, dusted with confectioners' sugar.