Preheat oven to 350°F (177°C). Line the bottom and sides of a 9×13-inch baking pan with parchment paper, leaving an overhang on the sides to lift the finished bars out (makes cutting easier!). Set aside.
Whisk the flour, baking powder, and salt together in a large bowl. Add the cubed butter and using a pastry cutter, two forks, or a food processor, cut in the butter until all the flour is coated and resembles pea-sized crumbles.
Whisk the egg, egg yolk, brown sugar, and vanilla together in a small bowl. Pour over the flour/butter mixture and gently mix together until the mixture resembles moist crumbly sand. Use your hands if needed.
You will have about 6 cups of the crust/crumble mixture. Set 2 cups aside. Pour the remaining into the prepared pan and flatten down with your hands or a flat spatula to form an even crust.
Mix the strawberries, granulated sugar, cornstarch, and lemon zest together. Spoon evenly over crust. Crumble the remaining butter/flour mixture on top and gently press down so it’s snug on the strawberry layer.
Bake for 45-50 minutes or until the top is lightly browned and the strawberry filling is bubbling on the sides. Remove from the oven and place the pan on a wire rack. Allow to cool completely.
Whisk the glaze ingredients together and drizzle on top. Lift the cooled bars out using the overhang on the sides. Cut into squares.
Cover and store leftover strawberry bars (with or without icing) at room temperature for up to 2 days or in the refrigerator for up to 1 week.
