In a large bowl, mix 1 cup sugar, flour, baking powder, cardamom, cinnamon, ginger, and salt. In the center of the bowl, add eggs, Greek yogurt, milk, vanilla extract, and melted butter. Stir until just combined. Pour batter into prepared baking dish. Lay halved, sliced pears on top of the batter. Slightly sink them into batter while keeping halves intact.