Preheat the oven to 350°F. Coat a 10-inch cast iron skillet with cooking spray.
In a medium bowl whisk together the flours, sugar, ginger, baking powder, and salt.
In a large bowl, beat eggs and egg white with an electric mixer for 2 minutes. Add the butter, milk, and half the thyme. Beat to combine. Stir in the flour mixture. Pour the batter into the prepared pan. Arrange the apricot halves over the surface of the batter, cut-side up. Sprinkle the remaining thyme over the top. Bake, about 35 minutes or until a toothpick inserted near the center comes out clean. Serve warm or at room temperature.