Halve the peaches and remove the pits. Slice into ¼-inch thick slices. Place a large skillet over medium heat. Add 1 tablespoon of the butter, the honey and 1 teaspoon of the ginger. Cook, stirring occasionally, until the syrup begins to bubble, about 2 minutes. Add the peach slices to the pan and toss gently with the syrup. Remove from the heat and set aside to cool slightly. When cool, transfer half of the peaches to a cutting board and coarsely chop.
Preheat the oven to 350˚ F. Grease muffin tins or line with paper liners. In a large bowl, combine the flours, sugars, baking powder, baking soda, salt, cinnamon and nutmeg. Whisk to blend. Melt the remaining 6 tablespoons of butter. In a liquid measuring cup, combine the milk, yogurt, egg, and the remaining 2 tablespoons of ginger. Whisk until well blended. Whisk in the melted butter. Pour the liquid mixture into the bowl with the dry ingredients and fold together just until incorporated and no dry streaks remain. Fold in the chopped peaches.
Scoop the batter into the prepared muffin pans filling each about 2/3 of the way full. Top each muffin with 1 or 2 of the ginger peach slices. Bake, rotating halfway through the baking time, until the muffins are lightly browned and just set, about 20-22 minutes total. Let cool in the pans about 5 minutes, gently remove from the pans and transfer to a wire rack to cool completely.
*Note: If you cannot find oat flour or would prefer not to purchase it, you can grind oats in your food processor until finely ground and use that instead.