Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish or line it with parchment paper for easy removal.
In a large mixing bowl, combine the flour, granulated sugar, salt, baking powder, and baking soda. Mix well.
Add the softened butter, egg, and vanilla extract to the dry ingredients. Mix until a crumbly dough forms. Reserve 1 cup of the dough for topping.
Press the remaining dough evenly into the bottom of the prepared baking dish to form the crust. Bake for 15 minutes, then remove from the oven and let cool slightly.
In another bowl, toss the sliced peaches with lemon juice, cornstarch, cinnamon, nutmeg, and brown sugar until well combined.
Spread the peach mixture evenly over the baked crust. Crumble the reserved dough over the top of the peaches.
Return the dish to the oven and bake for an additional 30-35 minutes, or until the topping is golden brown and the peaches are bubbly.
Allow the bars to cool completely in the pan before cutting into squares.