Preheat oven to 350°F. Line a 9×13-inch pan with parchment paper leaving a 1-inch overhang on two sides.

In a bowl, cream the cold cubed butter with 1 cup granulated sugar until mixture holds together; stir in 1 large egg and 1 teaspoon vanilla until combined.

Stir in 2 1/2 cups all-purpose flour and 1/2 teaspoon salt until crumbly; press about two-thirds of the dough evenly into the prepared pan for the base and refrigerate the remaining dough for the crumble.

Blind-bake the base at 350°F for 12–14 minutes until the edges are set and the center looks matte; remove from oven and keep oven at 350°F.

Peel and dice peaches to yield about 4 cups; place in a bowl with 1/3 cup granulated sugar, 1 tablespoon lemon juice, and 1 teaspoon vanilla and let sit 10–15 minutes to macerate.

Transfer peaches and juices to a medium saucepan; whisk in 2 tablespoons cornstarch and 1/2 teaspoon ground cinnamon until smooth and heat over medium, stirring, until mixture thickens and bubbles, about 3–5 minutes; remove from heat and cool slightly.

Spread the slightly cooled peach filling evenly over the pre-baked shortbread base.

In a bowl, combine the reserved dough with 1 cup rolled oats and 1/2 cup packed light brown sugar, breaking the dough into coarse crumbs, then scatter evenly over the peaches.

Bake assembled pan at 350°F for 25–30 minutes until the crumble is golden and the filling bubbles gently; remove and cool on a wire rack 1 hour, then chill 30–60 minutes for clean slices.

If using glaze, whisk 3/4 cup powdered sugar with 1 to 2 tablespoons milk and 1/4 teaspoon vanilla until smooth and drizzle over chilled bars, then slice into 12 squares using a warm, clean knife.