Preheat oven to 350 degrees. In a medium bowl, combine 3 tablespoons sugar, 1 tablespoon melted butter, grated ginger, cinnamon, orange zest, and dates. Add apples and toss to combine. Transfer mixture to an 8-inch square baking dish.
In a small bowl, combine gingersnaps with pecans, remaining sugar, oats, and remaining butter. Using your fingertips, work mixture to form a crumble topping. Distribute topping over apples. Cover dish tightly with aluminum foil. Bake until fruit mixture is bubbling, about 30 minutes. Uncover and continue baking until topping has browned and apples are tender when pierced with a paring knife, about 20 minutes. Let cool 10 minutes before serving with yogurt.