Combine the flour and salt in a large bowl. Add the stick of butter and cut in with a pastry cutter or fork, until the mixture resembles pebbles.

Add the ice water, a tablespoon at a time, and kneed to form a ball.

Roll dough into a ball and then press into a disc. Wrap in plastic wrap and refrigerate for an hour.

Core and quarter the apples. Using a mandoline or knife, cut into ⅛-inch thick slices.

Add the apples, brown sugar, ¼ cup granulated sugar, cardamom, cinnamon, and ginger to a large bowl. Toss to combine. Let sit for 45 minutes, tossing every 15 minutes. This will make the apples pliable for the rosette pattern.

Preheat the oven to 350 degrees F. When the dough is chilled, roll it out on a floured surface. Carefully move it over to cast iron pan or pie plate. Press the dough evenly across the bottom and sides of the pan.

Drain the apples. Arrange the apples in an overlapping pattern, starting from the outside and working in.

Sprinkle the remaining sugar and butter across the top of the tart.

Bake the tart for 50 to 60 minutes or until the apples and crust are golden.

Remove from oven and let cool for 15 minutes before cutting and serving.