Preheat the oven to 375 degrees. Melt the butter in a 9 x 13 baking dish.
In a medium bowl, combine the flour, ½ cup of the granulated sugar, the baking powder, and salt; add the honey, milk, and vanilla, stirring just until the dry ingredients are moistened. Pour the batter over the melted butter (do not stir).
In a large, nonreactive saucepan, bring the remaining ½ cup granulated sugar, the peach slices, brown sugar, lemon juice, and lime juice to a boil, stirring constantly, then remove from heat. Pour the peach mixture over the batter but do not stir. Sprinkle with cinnamon.
Bake for about 40 minutes or until golden brown, shielding the crust with foil during the last 10 minutes of baking so that it doesn’t overbrown. Serve warm with vanilla ice cream or whipped cream.