Preheat oven to 350°F (175°C). Line an 8x8-inch pan with parchment, leaving an overhang.
Whisk flour, sugar, salt, and baking powder. Cut in cold butter until coarse crumbs. Stir in egg to form a shaggy dough. Press two-thirds into pan for crust; reserve remaining crumbs.
Combine strawberries, rhubarb, sugar, cornstarch, and lemon juice in a saucepan. Cook over medium heat until thickened and glossy, about 6–8 minutes. Stir in vanilla if using.
Spread warm filling over crust, top with reserved crumbs. Bake 30–35 minutes until golden and bubbling. Cool completely to set.
Lift bars from pan using parchment overhang, slice into squares, and dust with powdered sugar or drizzle with glaze if desired.
Notes
Adjust sugar in the filling based on the sweetness of your strawberries and tartness of rhubarb.
Make the filling a day ahead to save time on bake day.
Freeze any extra bars for up to 2 months; thaw overnight in the fridge.