Step 1: In a large bowl, whisk together the flour, 1 tablespoon sugar, and salt. Cut in the cold butter using a pastry blender until the mixture resembles coarse meal.
Step 2: Gradually add ice water, one tablespoon at a time, mixing until the dough just begins to come together. Form into a disk, wrap in plastic, and refrigerate for at least 30 minutes.
Step 3: Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Step 4: In a medium bowl, toss the sliced pears, cranberries, 1/3 cup sugar, lemon juice, cinnamon, ginger, cardamom, and cornstarch together until the fruit is evenly coated.
Step 5: On a lightly floured surface, roll the chilled dough into a 12-inch circle. Transfer the dough to the prepared baking sheet.
Step 6: Mound the fruit mixture in the center of the dough, leaving about a 2-inch border around the edges.
Step 7: Gently fold the edges of the dough over the fruit, pleating the dough as you go. The center should remain open.
Step 8: Brush the edges of the crust with the beaten egg and sprinkle with coarse sugar.
Step 9: Bake for 35-40 minutes, or until the crust is golden brown and the fruit filling is bubbling.
Step 10: Allow the galette to cool on the baking sheet for at least 15 minutes before slicing and serving warm.