Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving an overhang on two sides.

Whisk 1 cup flour, 1 cup old-fashioned oats, 1/2 cup granulated sugar, 1/2 cup brown sugar, 1 teaspoon baking powder, 1/2 teaspoon cinnamon, and 1/4 teaspoon salt.

Stir in 1/2 cup melted butter and 1 teaspoon vanilla until a soft, sandy crumble forms.

Press two-thirds of the crumble firmly into the prepared 8x8-inch pan. Reserve the remaining one-third for the topping.

Toss 3 cups diced peaches, 1/3 cup granulated sugar, 1 tablespoon lemon juice, 1 tablespoon cornstarch, 1/2 teaspoon cinnamon, and 1/4 teaspoon nutmeg, if using, until coated.

Spread the 3-cup peach filling over the crust and sprinkle the reserved one-third crumble over the top.

Bake at 350°F for 38 to 45 minutes, until golden and bubbling at the edges. Cool at least 1 hour before lifting out and cutting into 9 bars.