• Preheat the oven to 350 degrees F. Line a 9x13-inch baking pan with parchment paper, leaving overhang on the sides for easy removal. Lightly spray with cooking spray.

Make the crust:

• In a large bowl, whisk together 1½ cups all-purpose flour, ½ cup granulated sugar, ½ teaspoon baking powder, and ⅛ teaspoon salt.
  
• Add 10 tablespoons cold unsalted butter, cubed and use a pastry cutter or your fingers to work it into the flour until the mixture resembles coarse crumbs. Add 1 large egg, lightly beaten, ½ teaspoon vanilla extract, and 1/2 teaspoon almond extract, mixing until the dough just comes together — it will be crumbly but should hold when pressed.
  
• Press the crust dough evenly into the prepared pan in a firm, even layer. Bake for 12 minutes until just set but not browned.
  

Make the peach filling:

• While the crust bakes, combine 5 cups peeled and diced fresh peaches, ripe but still firm, 2 tablespoons lemon juice, ¾ cup granulated sugar, ¼ teaspoon salt, ¼ cup all-purpose flour, 2 tablespoons cornstarch, ½ teaspoon ground cinnamon, 1 teaspoon vanilla extract, and ½ teaspoon almond extract in a large bowl. Stir to coat and let sit for 5 minutes.
  

Make the almond crumble:

• In a separate bowl, combine ¾ cup all-purpose flour, ½ cup almond flour, ⅓ cup light brown sugar, ¼ cup granulated sugar, and ¼ teaspoon salt. Add 6 tablespoons cold unsalted butter, cubed and use your fingers or a pastry cutter to work it in until large, sandy clumps form. Stir in ¼ teaspoon almond extract and ¼ cup finely chopped almonds.
  
• Pour the peach filling evenly over the par-baked crust, spreading gently with a spatula.
  
• Sprinkle the almond crumble topping evenly over the peach layer, covering it well.
  
• Bake for 45 to 50 minutes, until the topping is golden brown and the filling is bubbling around the edges.
• Remove from the oven and let cool completely in the pan — at least 3 hours — before lifting out and cutting into bars. For cleanest cuts, refrigerate for 1 hour after cooling.