Make The Filling: In a medium bowl, combine apple slices, granulated sugar, lemon juice, ground cinnamon and ground cardamom and toss to blend. Set aside.
Make Pie Crust: Combine flour, salt, and sugar in a food processor and pulse for a few seconds until combined (If you don’t have a food processor, you can do the whole process by hand in a mixing bowl). Add cold butter cubes and pulse until mixture becomes crumbly and resembles coarse meal. Add 2 tablespoons of cold water and pulse a few times to combine, adding more water as needed, one tablespoon at a time and keep pulsing until the dough starts to form. The dough at this time should be quite crumbly but still can hold together when you pinch it with your fingers. Do not process to the point that a large ball of dough is formed.
Transfer the dough to a floured surface and form into a ball. Use your hand to flatten slightly to form a 1-inch thick disc. Wrap the disc with plastic wrap and refrigerate for at least 1 hour. Soften slightly at room temperature before rolling out.
Place a disc of dough in between sheets of parchment paper. Use a rolling pin dusted with flour, rolling outwards from the center of the dough with an even pressure to make a large circle, around 12-inch in diameter. Remove the top sheet of parchment, then transfer the dough to a baking sheet lined with parchment paper.
Preheat oven to 400°F. Arrange apple slices in a circular pattern onto the crust, overlapping slightly, leaving about a 2-inch edge uncovered with apples. Using parchment as aid, fold the edge over the apples to seal. Start at one point in the round then move around the crust folding up about every 3-inches. Brush crust with milk. Sprinkle crust edges with sugar if desired.
Bake the apple galette for 25-30 minutes or until the crust is golden brown and the fruit becomes tender. Remove the galette from the oven and let it cool before slicing.
Serve with whipped cream or vanilla ice cream if desired.