Preheat the oven to 375°F (190°C). Grease an 8-inch square baking pan with cooking spray.
In a large bowl, whisk together 1 ½ cups of flour, ½ cup of white sugar, the baking powder, and salt.
Using two forks or a pastry cutter, cut in the cold butter until the mixture resembles coarse crumbs.
Slowly mix in the egg yolk and cold water; the dough will be very crumbly.
Press half of the crumble mixture firmly into the bottom of the prepared pan to create the crust. Reserve the remaining half.
In a separate bowl, stir together the sliced peaches, ½ cup of white sugar, 2 tablespoons of flour, the lemon juice, vanilla, cinnamon, and nutmeg until the peaches are well combined.
Spread the peach filling evenly over the crust in the pan.
Sprinkle the reserved crumble mixture over the top of the peaches.
Bake in the preheated oven for 30 to 38 minutes, until the topping is golden brown and the filling is set.
Let the bars cool completely to room temperature before cutting into 12 bars.
