For the Crust
Preheat the oven to 350F. Line a 9x9-inch pan with parchment paper. Combine the flour and sugar in a bowl then add the cubed butter and vanilla. Use a fork to combine. Press the mixture into the bottom of the pan and bake for 18-20 minutes or until a light golden brown.
For the Lemon Layer
Whisk ¾ cup of sugar and the cornstarch together. Add the lemon juice, 2 eggs, and corn syrup. Reserve 2/3 cup of this lemon filling and pour the rest over the hot crust. Bake for 15-17 minutes or just until set. Let cool at room temperature for 10-20 minutes. You need this layer to be set before adding the strawberry layer.
For the Strawberry Layer
Combine the strawberries, water, and 2 tablespoons sugar in a saucepan. Cook over medium heat for 5 minutes or until the berries soften. Use an emulsion blender to blend until smooth. Whisk in the reserved lemon mixture then the remaining egg. Carefully pour the strawberry mixture over the lemon. Bake for 15 minutes or just until set. Cool completely then refrigerate for at least 4 hours before removing from the pan and cutting into bars. Garnish with powdered sugar, if desired.