How to Make It
Preheat the oven to 400°. In a mini processor, pulse 3/4 cup of the almonds until finely ground. Transfer to a medium bowl. Pulse the remaining 1/4 cup of almonds, until coarsely chopped. Transfer to the bowl, add the granulated sugar, flour and salt and toss gently to combine.
In another bowl, using a handheld mixer, beat the 4 tablespoons of butter until creamy. Add the almond mixture and beat until blended. Add the eggs one at a time, beating well after each addition. Beat in the rum.
Spread the almond filling in the Baked Pastry Shell. Arrange the apple slices on top in concentric circles. Brush the apple slices with the melted butter and sprinkle with the brown sugar.
Bake the tart for 1 hour, until the filling is set and the apples are browned and tender. Transfer the tart to a rack and let cool slightly. Remove the ring and serve the tart warm or at room temperature.