Preheat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper or lightly grease it.
In a large bowl, whisk together the flour, sugar, baking powder, and salt.
Cut in the cold butter using a pastry cutter or your fingertips until the mixture resembles coarse crumbs.
Stir in the egg and vanilla extract until the mixture becomes crumbly.
Press about two-thirds of the crumb mixture firmly into the bottom of the prepared baking pan to form the crust.
In another bowl, combine the diced peaches, sugar, cornstarch, lemon juice, cinnamon, and nutmeg. Toss gently until evenly coated.
Spread the peach mixture evenly over the crust.
Sprinkle the remaining crumb mixture evenly over the peaches.
Bake for 40–45 minutes, or until the topping is golden brown and the peach filling is bubbling.
Allow the bars to cool completely before slicing into squares.
Dust with powdered sugar or serve with vanilla ice cream if desired.