Preheat the oven to 350 degrees F, and grease a 9-inch cake pan. (If substituting a 9-inch pie plate, it will need to be the deep dish variety to accommodate the batter; could also use an 8-inch square pan.)
Toss the peaches with the nutmeg and 2 tablespoons sugar. Set aside.
With a handheld or stand mixer, cream together the butter and remaining sugar. Add the egg, yogurt, and extracts, and stir to combine.
In a separate bowl, combine the flours, baking powder, baking soda and salt. Add the flour mixture to the butter mixture, and mix until smooth, taking care not to overbeat.
Fold in the peaches with all of the juices, and then transfer the batter to the prepared pan. Sprinkle the turbinado sugar over the top.
Bake for 10 minutes, and then reduce the oven heat to 325 degrees F and bake for an additional 30-40 minutes. Check a little early and allow for additional baking time depending on oven and various options used. The cake should be just cooked through the center and pass the toothpick test.