Preheat oven to 180°C (350°F). Line a 9x13 inch pan with parchment, leaving overhang on two sides. Grease lightly.
Combine flour, oats, both sugars, baking powder, cinnamon, and salt in a large bowl.
Add cold butter cubes and vanilla. Work butter into the dry ingredients until the mixture resembles coarse, uneven crumbs with some pea-sized butter pieces visible.
Press two-thirds of the mixture firmly into the prepared pan using the flat bottom of a measuring cup.
Toss raspberries with sugar, cornstarch, lemon juice, lemon zest, and vanilla until coated.
Spread raspberry mixture evenly over the pressed base.
Scatter remaining crumble loosely over the raspberry layer in uneven clumps. Do not press down.
Bake 38–42 minutes until topping is deep golden and filling is visibly bubbling at the edges.
Cool completely in the pan for at least 2 hours before cutting. Refrigerate for 30 minutes after cooling for the cleanest cuts.
Lift out using parchment overhang. Cut into 16 bars with a sharp knife, cleaning between cuts.
Dust with powdered sugar, drizzle with white chocolate, or scatter flaky sea salt if desired.