First, preheat your oven to 350°F (175°C). To make removing the bars easy later on, line a 9x13-inch baking pan with parchment paper. Leave some paper hanging over the sides to use as handles for lifting the bars out once they have cooled completely.
In a large bowl, whisk together the flour, baking powder, salt, granulated sugar, and brown sugar. Add the cold, cubed butter to the dry ingredients. Using a pastry blender or your fingertips, cut the butter into the mixture until it resembles coarse crumbs with some pea-sized pieces remaining.
Take out 1 ½ cups of the crumb mixture and set it aside for the topping. Press the rest of the mixture firmly and evenly into the bottom of your prepared baking pan. This will form the sturdy base for your peach bars. Bake it for 12 minutes to par-bake the crust.
While the crust is in the oven, prepare the delicious peach filling. In a separate bowl, gently toss the sliced peaches with the cornstarch, sugar, lemon juice, cinnamon, and optional ginger. Let this mixture sit for about five minutes to allow the juices to release and the flavors to meld.
Remove the partially baked crust from the oven. Carefully spread the peach mixture in an even layer over the warm crust, making sure to include all the delicious juices. Now, take the reserved crumb mixture, stir in the rolled oats, and sprinkle it evenly over the peaches.
Return the pan to the oven and bake for an additional 30-35 minutes. You'll know the bars are done when the oat topping is golden brown and the peach filling is bubbling around the edges. The aroma alone will tell you something wonderful is happening in your oven.
Once baked, remove the pan and place it on a wire rack to cool completely. This step is crucial for clean slices. If you try to cut them while warm, they will fall apart. Once fully cooled, use the parchment paper handles to lift the entire block out of the pan and cut it into 12 bars.