In a small bowl, whisk together the all-purpose and whole-wheat flours, baking powder, baking soda, cinnamon, ginger, salt and lemon zest; set aside. In a small saucepan over medium heat, combine the 1/4 cup of butter, brown sugar and maple syrup. Stir until the butter is melted and the sugar is dissolved. Pour the syrup into the bottom of a well-buttered 9-inch round cake pan. Arrange the apricot halves evenly on top, skin side down.
In the bowl of a stand mixer (or in a large bowl using a handheld mixer) cream the 6 tablespoons of butter with the coconut sugar for 5 minutes. Add the eggs, one at a time, until combined well. Add the vanilla. Fold in one-third of the yogurt alternately with one-third of the flour mixture, repeating twice with both, until just combined.
Using an offset spatula or the back of a soup spoon, spread the batter evenly over the apricots, right to the edge of the pan. Bake in a 350º F oven until the top of the cake is light brown and bounces back when lightly touched, 35 to 40 minutes. Place the pan on a rack for 5 minutes. Run a sharp paring knife between the cake and the edge of the pan. Carefully turn the cake over onto a serving plate. Serve warm or at room temperature with vanilla ice cream or crème fraîche.