Preheat oven to 375°F (190°C). Spray a 9-inch square baking pan with baking spray with flour. Line pan with parchment paper, letting excess extend over all sides of pan.

For dough: In a medium bowl, whisk together melted butter, sugar, and vanilla.

In another medium bowl, whisk together flour, oats, baking powder, and salt. Gradually stir flour mixture into butter mixture until combined. Reserve ¾ cup (about 230 grams) dough in a small bowl for topping; press remaining dough into bottom of prepared pan.

Bake until edges are lightly browned, about 15 minutes. Let cool while preparing filling.

For filling: In a medium saucepan, bring blackberries, sugar, and lemon zest to a boil over medium heat; cook, stirring frequently, until blackberries have broken down and released most of their juices, 8 to 10 minutes.

In another small bowl, whisk together cornstarch and lemon juice. Stir cornstarch mixture into blackberry mixture; cook, stirring constantly, until mixture becomes thick and translucent, 2 to 3 minutes. Pour filling onto prepared crust. Crumble reserved dough on top.

Bake until topping is golden brown and filling is bubbling, 20 to 25 minutes, loosely covering with foil after 15 minutes of baking to prevent excess browning. Let cool completely in pan on a wire rack.

Using excess parchment paper as handles, remove from pan, and cut into bars. Store in an airtight container for up to 3 days.