Preheat the oven to 375°F (190°C).
Line an 8×8-inch baking pan with parchment paper, allowing the edges to hang over the sides.
In a medium bowl, combine the flour, baking powder, salt, and 1/2 cup sugar.
Cut the cold butter into the flour mixture using a pastry cutter, fork, or food processor until pea-sized crumbs form.
Stir together the beaten egg and vanilla. Add to the crumb mixture and mix until crumbly.
Press half of the mixture firmly into the bottom of the prepared pan.
In another bowl, mix the strawberries with 1/3 cup sugar and cornstarch until evenly coated.
Spread the strawberry filling evenly over the crust.
Sprinkle the remaining crumb mixture over the top.
Bake the Strawberry Crumb Bars for 38–45 minutes, or until the top is lightly golden.
Allow the bars to cool completely before slicing. Chill before serving for cleaner cuts.