Preheat your oven to 350°F (175°C) and line a 9x13-inch baking pan with parchment paper, leaving some overhang for easy removal.

In a large mixing bowl, combine the flour, oats, granulated sugar, brown sugar, baking powder, and salt. Stir until evenly mixed.

Add the melted butter to the dry ingredients and mix until the mixture resembles coarse crumbs. Reserve 1 cup of this mixture for the crumble topping.

Press the remaining crust mixture firmly into the bottom of the prepared pan to form an even base layer.

In a medium bowl, combine the diced peaches, 1/4 cup granulated sugar, cornstarch, lemon juice, and vanilla extract. Stir gently until the peaches are evenly coated.

In another bowl, beat the softened cream cheese, 1/4 cup granulated sugar, egg, and 1/2 teaspoon vanilla extract until smooth and creamy.

Spread the cream cheese mixture evenly over the crust layer in the pan.

Pour the peach mixture over the cream cheese layer, spreading it evenly.

Sprinkle the reserved crumble mixture over the peaches to create the topping.

Bake in the preheated oven for 40-45 minutes, or until the top is golden brown and the filling is set.

Remove the pan from the oven and allow the bars to cool completely in the pan before lifting them out using the parchment paper overhang.

Once cooled, cut into bars and serve. Store leftovers in an airtight container in the refrigerator.