How to Make It
Make Dough: Combine flour, sugar, and salt in a food processor. Pulse to incorporate. Add butter and shortening and pulse until butter is broken down into the size of small pebbles. Add 4 tablespoons ice water and pulse about 10 times or until dough begins to clump. If dough isn’t clumping, add remaining tablespoon of water and pulse to combine. Press dough into one round disc about 2 inches thick, wrap in plastic wrap, and refrigerate for at least 1 hour.
Cut plums into 1/2-inch thick segments. Place plum pieces, honey, lemon juice, cornstarch, cardamom, and salt in a bowl and toss to coat.
Line a baking sheet with parchment paper. On a well floured surface, roll dough into a 14-inch wide circle. Transfer circle to lined baking sheet. Leaving a 1 1/2-inch margin around the perimeter of the circle, evenly spread the gingersnap crumbs inside the circle of dough. Place plum pieces on top of the circle of crumbs and pour any accumulated juices on top of the plums. Lifting one side of the circle, fold the dough up so it just covers a small portion of the circle of fruit. A few inches around from that fold, grab the dough again and lift it up to fold it partially over the fruit, creating a pleat in the dough and beginning to encase the fruit in dough. Repeat around the circle until it is fully encased. Place in freezer for 20 minutes.
Preheat oven to 425°F. Brush dough of galette with milk or water and sprinkle raw sugar on the surface of the exposed dough. Transfer galette to oven, rotating halfway through baking, until the fruit is cooked through and the bottom of the galette is well browned, about 25 minutes. Allow galette to cool to room temperature before slicing and serving.