Position a rack in the center of the oven and preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper or foil, leaving an overhang on the ends. Lightly grease the pan.
In a large bowl, combine the flour, oats, brown sugar, salt, and baking powder. Add the softened butter and use your fingers or a pastry cutter to blend the butter completely into the dry ingredients until a crumbly mixture forms.
Transfer 2 cups of the crumb mixture to another bowl and reserve for the topping.
Mix the egg white into the remaining crumb mixture. Press evenly into the bottom of the prepared pan to form the crust.
Bake the crust for 10–12 minutes, until the surface looks dry and is just beginning to set.
While the crust bakes, prepare the strawberry filling. Add the diced strawberries to a large bowl.
In a small bowl, whisk together the granulated sugar and cornstarch. Sprinkle over the strawberries, then add the lemon juice and vanilla. Gently toss until the strawberries are evenly coated.
Spread the strawberry mixture evenly over the hot crust, including any juices in the bowl.
Sprinkle the reserved crumb mixture evenly over the strawberries, squeezing some of the mixture between your fingers as you work to create larger crumb clusters.
Return the pan to the oven and bake for 30–35 minutes, or until the strawberry filling is bubbling around the edges and the crumb topping is lightly golden brown.
Transfer the pan to a wire rack and allow the bars to cool completely, about 1 hour.
Once completely cooled, use the parchment or foil overhang to lift the bars from the pan. Cut into 24 bars and serve.