Heat the oven to 350°F. Put the butter in a 10-inch Dutch oven or a deep 3-quart baking dish and melt it; remove the dish once melted.
To peel the peaches, boil them for 1 minute, move them to an ice bath, slip off the skins, and slice them about 1/3 inch thick. A vegetable peeler may also be used.
Stir the peaches with the honey, cornstarch, vanilla, cinnamon, and ginger. Set the fruit aside while the topping is mixed.
Whisk the sugar, white whole wheat flour, all-purpose flour, baking powder, and salt in a separate bowl. Whisk in the milk. Pour the batter over the melted butter without stirring, then spoon the peaches and their juices over the batter without stirring.
Bake for 50 to 60 minutes, until the topping is deep golden at the edges and a toothpick inserted into the topping, not the fruit, comes out clean. Serve warm with vanilla ice cream, whipped cream, Greek yogurt, or heavy cream.