Preheat oven to 350 degrees F. In a medium bowl stir together flour, baking powder, ginger, cinnamon, baking soda, and salt; set aside. Place the 3 tablespoons butter in a 10x2-inch cast-iron or other heavy oven-going skillet. Place skillet in the oven for 3 to 5 minutes or until butter is melted. Remove from oven. Carefully tip skillet to coat the sides with butter.
Sprinkle brown sugar evenly over bottom of skillet. Arrange orange sections over brown sugar. Top evenly with cranberries.
In a large bowl combine eggs, yogurt, granulated sugar, the melted butter, and vanilla. Add flour mixture to egg mixture, one-third at a time, stirring just until combined after each addition. Spoon batter into skillet, spreading to cover fruit.
Bake for 35 to 40 minutes or until a wooden toothpick inserted in the center of cake comes out clean. Cool in skillet on a wire rack for 3 to 4 minutes. Run a knife around edges of cake to loosen. Invert a serving platter over skillet. Carefully turn platter and skillet over together; remove skillet. Replace any fruit that remains in skillet. Serve warm or at room temperature.